Finite Group Databasebeta

← Group #6715

Character table — Group #6715

Order 240.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size112222222222222224444444444444444444444303060
order12345561010151515153030303026610101010122020303030303030303060606060882
χ1111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1
χ311111111111111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1
χ411111111111111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-11
χ52222−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+52−1+522−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+52000
χ62222−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−522−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+52000
χ72222−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1−52−1−522−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−52000
χ82222−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+522−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52000
χ9222-222222222222220000000-2-2-200000000-2-2-2-2000
χ10222-2−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116-21+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+ζ1161+521+521−521−52000
χ11222-2−1−52−1+522−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116-21+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−ζ1161+521+521−521−52000
χ12222-2−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92-21−521+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+ζ921−521−521+521+52000
χ13222-2−1+52−1−522−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92-21−521+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−ζ921−521−521+521+52000
χ1422-1222-122-1-1-1-1-1-1-1-12-1-12222-122-1-1-1-1-1-1-1-1-1-1-1-1000
χ1522-1222-122-1-1-1-1-1-1-1-1-211-2-2-2-2-12211111111-1-1-1-1000
χ1622-12−1−52−1+52-1−1−52−1+52−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1162-1-1−1−52−1−52−1+52−1+52-1−1−52−1+52−ζ52−ζ68−ζ28−ζ92−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116000
χ1722-12−1−52−1+52-1−1−52−1+52−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116-2111+521+521−521−52-1−1−52−1+52ζ52+ζ68ζ28+ζ92ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116ζ44+ζ76ζ4+ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116000
χ1822-12−1−52−1+52-1−1−52−1+52−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ762-1-1−1−52−1−52−1+52−1+52-1−1−52−1+52−ζ28−ζ92−ζ52−ζ68−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76000
χ1922-12−1−52−1+52-1−1−52−1+52−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76-2111+521+521−521−52-1−1−52−1+52ζ28+ζ92ζ52+ζ68ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76ζ4+ζ116ζ44+ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76000
χ2022-12−1+52−1−52-1−1+52−1−52−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ682-1-1−1+52−1+52−1−52−1−52-1−1+52−1−52−ζ44−ζ76−ζ4−ζ116−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68000
χ2122-12−1+52−1−52-1−1+52−1−52−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68-2111−521−521+521+52-1−1+52−1−52ζ44+ζ76ζ4+ζ116ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68ζ28+ζ92ζ52+ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68000
χ2222-12−1+52−1−52-1−1+52−1−52−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ922-1-1−1+52−1+52−1−52−1−52-1−1+52−1−52−ζ4−ζ116−ζ44−ζ76−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92000
χ2322-12−1+52−1−52-1−1+52−1−52−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92-2111−521−521+521+52-1−1+52−1−52ζ4+ζ116ζ44+ζ76ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92ζ52+ζ68ζ28+ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92000
χ2422-1-222-122-1-1-1-1-1-1-1-10−i3i300001-2-2−i3i3i3−i3i3−i3−i3i31111000
χ2522-1-222-122-1-1-1-1-1-1-1-10i3−i300001-2-2i3−i3−i3i3−i3i3i3−i31111000
χ2622-1-2−1−52−1+52-1−1−52−1+52−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1160−i3i3ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ11611+521−52ζ52−ζ68−ζ28+ζ92−ζ52+ζ68ζ28−ζ92ζ44−ζ76ζ4−ζ116−ζ44+ζ76−ζ4+ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116000
χ2722-1-2−1−52−1+52-1−1−52−1+52−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ116−ζ52−ζ68−ζ28−ζ92−ζ44−ζ76−ζ4−ζ1160i3−i3−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ11611+521−52−ζ52+ζ68ζ28−ζ92ζ52−ζ68−ζ28+ζ92−ζ44+ζ76−ζ4+ζ116ζ44−ζ76ζ4−ζ116ζ52+ζ68ζ28+ζ92ζ44+ζ76ζ4+ζ116000
χ2822-1-2−1−52−1+52-1−1−52−1+52−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ760−i3i3−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ92ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ11611+521−52ζ28−ζ92−ζ52+ζ68−ζ28+ζ92ζ52−ζ68−ζ4+ζ116−ζ44+ζ76ζ4−ζ116ζ44−ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76000
χ2922-1-2−1−52−1+52-1−1−52−1+52−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ76−ζ28−ζ92−ζ52−ζ68−ζ4−ζ116−ζ44−ζ760i3−i3ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ92−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ11611+521−52−ζ28+ζ92ζ52−ζ68ζ28−ζ92−ζ52+ζ68ζ4−ζ116ζ44−ζ76−ζ4+ζ116−ζ44+ζ76ζ28+ζ92ζ52+ζ68ζ4+ζ116ζ44+ζ76000
χ3022-1-2−1+52−1−52-1−1+52−1−52−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ680−i3i3ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ9211−521+52−ζ44+ζ76−ζ4+ζ116ζ44−ζ76ζ4−ζ116−ζ28+ζ92ζ52−ζ68ζ28−ζ92−ζ52+ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68000
χ3122-1-2−1+52−1−52-1−1+52−1−52−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ68−ζ44−ζ76−ζ4−ζ116−ζ28−ζ92−ζ52−ζ680i3−i3−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ9211−521+52ζ44−ζ76ζ4−ζ116−ζ44+ζ76−ζ4+ζ116ζ28−ζ92−ζ52+ζ68−ζ28+ζ92ζ52−ζ68ζ44+ζ76ζ4+ζ116ζ28+ζ92ζ52+ζ68000
χ3222-1-2−1+52−1−52-1−1+52−1−52−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ920−i3i3−ζ4−ζ44+ζ76+ζ116ζ4+ζ44−ζ76−ζ116−ζ28+ζ52−ζ68+ζ92ζ28−ζ52+ζ68−ζ9211−521+52ζ4−ζ116ζ44−ζ76−ζ4+ζ116−ζ44+ζ76−ζ52+ζ68ζ28−ζ92ζ52−ζ68−ζ28+ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92000
χ3322-1-2−1+52−1−52-1−1+52−1−52−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ92−ζ4−ζ116−ζ44−ζ76−ζ52−ζ68−ζ28−ζ920i3−i3ζ4+ζ44−ζ76−ζ116−ζ4−ζ44+ζ76+ζ116ζ28−ζ52+ζ68−ζ92−ζ28+ζ52−ζ68+ζ9211−521+52−ζ4+ζ116−ζ44+ζ76ζ4−ζ116ζ44−ζ76ζ52−ζ68−ζ28+ζ92−ζ52+ζ68ζ28−ζ92ζ4+ζ116ζ44+ζ76ζ52+ζ68ζ28+ζ92000
χ342-22022-2-2-22222-2-2-2-200000000000000000000002−20
χ352-22022-2-2-22222-2-2-2-20000000000000000000000−220
χ364-440−1−5−1+5-41+51−5−1−5−1−5−1+5−1+51+51+51−51−50000000000000000000000000
χ374-440−1+5−1−5-41−51+5−1+5−1+5−1−5−1−51−51−51+51+50000000000000000000000000
χ384-4-20442-4-4-2-2-2-222220000000000000000000000000
χ394-4-20−1−5−1+521+51−5−2ζ52−2ζ68−2ζ28−2ζ92−2ζ44−2ζ76−2ζ4−2ζ1162ζ52+2ζ682ζ28+2ζ922ζ44+2ζ762ζ4+2ζ1160000000000000000000000000
χ404-4-20−1−5−1+521+51−5−2ζ28−2ζ92−2ζ52−2ζ68−2ζ4−2ζ116−2ζ44−2ζ762ζ28+2ζ922ζ52+2ζ682ζ4+2ζ1162ζ44+2ζ760000000000000000000000000
χ414-4-20−1+5−1−521−51+5−2ζ44−2ζ76−2ζ4−2ζ116−2ζ28−2ζ92−2ζ52−2ζ682ζ44+2ζ762ζ4+2ζ1162ζ28+2ζ922ζ52+2ζ680000000000000000000000000
χ424-4-20−1+5−1−521−51+5−2ζ4−2ζ116−2ζ44−2ζ76−2ζ52−2ζ68−2ζ28−2ζ922ζ4+2ζ1162ζ44+2ζ762ζ52+2ζ682ζ28+2ζ920000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.