Finite Group Databasebeta

← Group #14513277

Character table — Group #14513277

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222244444668888101012121212121212121212121212161616161616161616161616161616161616202424242424242424242424242424242424246060606080808080120120120
order122255101010101010210101010443666444448820202020202020206615153030303030303030303030303030248202020202020202040404040404040404488661212248
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-11-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1
χ311111111111111111111111-1-11111111111111111111111111111111-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-11-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ5111111111111-1-1-1-1-11111111111-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-1111-1-1
χ6111111111111-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11-1-1-1-111-111
χ7111111111111-1-1-1-1-1111111-1-111-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-1-111
χ8111111111111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111-11111-1-11-1-1
χ92222222222222222222-1-1-1-1220020022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-120000000000000000002200-1-1-1-1000
χ102222222222222222222-1-1-1-1-2-20020022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2000000000000000000-2-2001111000
χ11222222222222-2-2-2-2-222-1-1-1-12200-20022-2-2-2-22211-1-1-1-1-1-1-1-111111111-2000000000000000000-220011-1-1000
χ12222222222222-2-2-2-2-222-1-1-1-1-2-200-20022-2-2-2-22211-1-1-1-1-1-1-1-11111111120000000000000000002-200-1-111000
χ132222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522−1−52−1−52−1+52−1+522222220022222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52022−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000
χ142222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522−1−52−1−52−1+52−1+5222222200-2-22-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000
χ152222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-21+521+521−521−522222220022-222−1−52−1+521+521+521−521−52−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−520-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000
χ162222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-21+521+521−521−5222222200-2-2-2-2-2−1−52−1+521+521+521−521−52−1−52−1+52-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521+521+521−521−521−521−520221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200000000000
χ172222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522−1+52−1+52−1−52−1−522222220022222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52022−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000
χ182222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522−1+52−1+52−1−52−1−5222222200-2-22-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000
χ192222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-21−521−521+521+522222220022-222−1+52−1−521−521−521+521+52−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+520-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000
χ202222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-21−521−521+521+5222222200-2-2-2-2-2−1+52−1−521−521−521+521+52−1+52−1−52-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521−521−521+521+521+521+520221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000000000
χ212-22-2222-2-22-2-2000002-222-2-2002i−2i02i−2i220000-2-200222-2-22-2-2000000000002i−2i2i−2i00002i−2i2i−2i000000000000000
χ222-22-2222-2-22-2-2000002-222-2-200−2i2i0−2i2i220000-2-200222-2-22-2-200000000000−2i2i−2i2i0000−2i2i−2i2i000000000000000
χ232-22-2−1−52−1+52−1−521+521+52−1+521−521−520−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1162-222-2-2002i−2i02i−2i−1−52−1+52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1161+521−5200−1−52−1+52−1−521+521+52−1+521−521−52−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116000−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ94−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ9400000000000
χ242-22-2−1−52−1+52−1−521+521+52−1+521−521−520−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1162-222-2-200−2i2i0−2i2i−1−52−1+52−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ1161+521−5200−1−52−1+52−1−521+521+52−1+521−521−52−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116000ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ94ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ9400000000000
χ252-22-2−1−52−1+52−1−521+521+52−1+521−521−520ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1162-222-2-2002i−2i02i−2i−1−52−1+52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1161+521−5200−1−52−1+52−1−521+521+52−1+521−521−52ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116000−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ94−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ9400000000000
χ262-22-2−1−52−1+52−1−521+521+52−1+521−521−520ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1162-222-2-200−2i2i0−2i2i−1−52−1+52ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ1161+521−5200−1−52−1+52−1−521+521+52−1+521−521−52ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116000ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ94ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ9400000000000
χ272-22-2−1+52−1−52−1+521−521−52−1−521+521+520ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ922-222-2-2002i−2i02i−2i−1+52−1−52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ921−521+5200−1+52−1−52−1+521−521−52−1−521+521+52ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92000−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ118−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ11800000000000
χ282-22-2−1+52−1−52−1+521−521−52−1−521+521+520ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ922-222-2-200−2i2i0−2i2i−1+52−1−52ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ921−521+5200−1+52−1−52−1+521−521−52−1−521+521+52ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92000ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ118ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ11800000000000
χ292-22-2−1+52−1−52−1+521−521−52−1−521+521+520−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ922-222-2-2002i−2i02i−2i−1+52−1−52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ921−521+5200−1+52−1−52−1+521−521−52−1−521+521+52−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92000−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ118−ζ14−ζ46−ζ86−ζ94ζ14+ζ46+ζ86+ζ94−ζ22−ζ38−ζ62−ζ118ζ22+ζ38+ζ62+ζ118ζ14−ζ46−ζ86+ζ94−ζ14+ζ46+ζ86−ζ94ζ22−ζ38+ζ62−ζ118−ζ22+ζ38−ζ62+ζ11800000000000
χ302-22-2−1+52−1−52−1+521−521−52−1−521+521+520−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ922-222-2-200−2i2i0−2i2i−1+52−1−52−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ921−521+5200−1+52−1−52−1+521−521−52−1−521+521+52−ζ4−ζ44+ζ76+ζ116−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ28−ζ52+ζ68−ζ92000ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ118ζ14+ζ46+ζ86+ζ94−ζ14−ζ46−ζ86−ζ94ζ22+ζ38+ζ62+ζ118−ζ22−ζ38−ζ62−ζ118−ζ14+ζ46+ζ86−ζ94ζ14−ζ46−ζ86+ζ94−ζ22+ζ38−ζ62+ζ118ζ22−ζ38+ζ62−ζ11800000000000
χ3133333333333333333-1-100003311-1-1-1-1-1-1-1-1-1-1-100000000000000000031-111111111-1-1-1-1-1-1-1-1-1-1-1-1000011-1
χ3233333333333333333-1-1000033-1-1-111-1-1-1-1-1-1-1-10000000000000000003-11-1-1-1-1-1-1-1-111111111-1-1110000-1-11
χ3333333333333333333-1-10000-3-311-1-1-1-1-1-1-1-1-1-1-1000000000000000000-31-111111111-1-1-1-1-1-1-1-111110000-1-11
χ3433333333333333333-1-10000-3-3-1-1-111-1-1-1-1-1-1-1-1000000000000000000-3-11-1-1-1-1-1-1-1-11111111111-1-1000011-1
χ35333333333333-3-3-3-3-3-1-1000033111-1-1-1-11111-1-1000000000000000000-3-111111-1-1-1-1-1-1-1-111111-1-1-100001-11
χ36333333333333-3-3-3-3-3-1-1000033-1-1111-1-11111-1-1000000000000000000-31-1-1-1-1-111111111-1-1-1-11-1110000-11-1
χ37333333333333-3-3-3-3-3-1-10000-3-3111-1-1-1-11111-1-10000000000000000003-111111-1-1-1-1-1-1-1-11111-11110000-11-1
χ38333333333333-3-3-3-3-3-1-10000-3-3-1-1111-1-11111-1-100000000000000000031-1-1-1-1-111111111-1-1-1-1-11-1-100001-11
χ394444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+54−1−5−1−5−1+5−1+544-2-2-2-20000400−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-2-21+521−521+521+521+521−521−521−521+521+521+521+521−521−521−521−52000000000000000000000000000000
χ404444−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-41+51+51−51−544-2-2-2-20000-400−1−5−1+51+51+51−51−5−1−5−1+5221+521−521+521+521+521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000000000000000000000000
χ414444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−54−1+5−1+5−1−5−1−544-2-2-2-20000400−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-2-21−521+521−521−521−521+521+521+521−521−521−521−521+521+521+521+52000000000000000000000000000000
χ424444−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-41−51−51+51+544-2-2-2-20000-400−1+5−1−51−51−51+51+5−1+5−1−5221−521+521−521−521−521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000000000000000000000000
χ4344-4-444-44-4-44-400000001-1-114-40000000000000−i3i311-11-1-11-1−i3i3−i3i3−i3i3−i3i300000000000000000000000−i3i31-1000
χ4444-4-444-44-4-44-400000001-1-114-40000000000000i3−i311-11-1-11-1i3−i3i3−i3i3−i3i3−i300000000000000000000000i3−i31-1000
χ4544-4-444-44-4-44-400000001-1-11-440000000000000−i3i311-11-1-11-1−i3i3−i3i3−i3i3−i3i300000000000000000000000i3−i3-11000
χ4644-4-444-44-4-44-400000001-1-11-440000000000000i3−i311-11-1-11-1i3−i3i3−i3i3−i3i3−i300000000000000000000000−i3i3-11000
χ4744-4-444-44-4-44-40000000-222-24-4000000000000000-2-22-222-22000000000000000000000000000000000-22000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.