Finite Group Databasebeta

← Group #10702212

Character table — Group #10702212

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222234444444466666661212121212121212666688888888121212122424242424242424242424242424242488888888242424242424242424242424242424242222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
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χ161-1-1-1111-111-1-11111-1-11-1-111-1-1-1-1111-1-111-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
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χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-2-2-2-2222-22-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2422222222-2-2-2-2222-22-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2522222222-2-2-2-22-2-22-2222-2222222222222222-2-2-2-200000000-2-2-2-2000000000000000000000000000000000000000000002-22-200000000
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χ2722222222-2-2-2-2-122-22-2-2-22-1-1-1-1-1-1-111111111111122-2-222-2-2-1-1-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−30000000000000000
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χ2922222222-2-2-2-2-122-22-2-2-22-1-1-1-1-1-1-1111111111111-2-222-2-222-1-1-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ3022222222-2-2-2-2-122-22-2-2-22-1-1-1-1-1-1-1111111111111-2-222-2-222-1-1-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ31222-22-2-2-22-22-222-2222-2-2-2-2-222-2-222222-2-2-2-22-22-2000000002-22-200000000000000000000000000000000000000002-22-2000000000000
χ32222-22-2-2-22-22-222-2222-2-2-2-2-222-2-222222-2-2-2-22-22-2000000002-22-20000000000000000000000000000000000000000-22-22000000000000
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χ40222-22-2-2-2-22-2222-2-22-222-2-2-222-2-22-2-2-2-22222-22-22000000002-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ41222-22-2-2-2-22-222-222-22-2-22-2-222-2-222222-2-2-2-2-22-2200000000-22-2200000000000000002i−2i2i−2i00002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ42222-22-2-2-2-22-222-222-22-2-22-2-222-2-222222-2-2-2-2-22-2200000000-22-220000000000000000−2i2i−2i2i0000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ43222-22-2-2-2-22-22-1-222-22-2-2211-1-111-1-1-1-1-111111-11-1000000001-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32i−2i2i−2i0000−iii−i−iii−i3−3−333−3−330000000000000000
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χ472-2-222-2-222-2-2222-22-2-2-222-2-2-2-222222-2-2-2-2222-2-22000000002-2-2200000000000000000000000000000000000000002-2-22000000000000
χ482-2-222-2-222-2-2222-22-2-2-222-2-2-2-222222-2-2-2-2222-2-22000000002-2-220000000000000000000000000000000000000000-222-2000000000000
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χ552-2-222-2-22-222-222-2-2-222-22-2-2-2-2222-2-22222-2-2-222-2000000002-2-220000000000000000000000000000000000000000000000002-2-220000
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χ642-2-2-2222-222-2-22-2-2-222-22222-2-2-2-22-2-222-2-22222-2-200000000-2-2220000000000000000000000000000000000000000000000000000-222-2
χ652-2-2-2222-222-2-2-1222-2-22-2-2-1-11111-1-1-111-1-111-1-1112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii0000000000000000
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χ8344-44-44-4-40000-200000000-22-22-22223−2323−2323−2323−23000000−2i22i200−2i22i20000i6−i6i6−i6i2−i2i2−i2i6−i6i6−i6i2−i2i2−i20000000000000000000000000000000000000000
χ8444-44-44-4-40000-200000000-22-22-22223−2323−2323−2323−230000002i2−2i2002i2−2i20000−i6i6−i6i6−i2i2−i2i2−i6i6−i6i6−i2i2−i2i20000000000000000000000000000000000000000
χ8544-44-44-4-40000-200000000-22-22-222−2323−2323−2323−2323000000−2i22i200−2i22i20000−i6i6−i6i6i2−i2i2−i2−i6i6−i6i6i2−i2i2−i20000000000000000000000000000000000000000
χ8644-44-44-4-40000-200000000-22-22-222−2323−2323−2323−23230000002i2−2i2002i2−2i20000i6−i6i6−i6−i2i2−i2i2i6−i6i6−i6−i2i2−i2i20000000000000000000000000000000000000000
χ8744-4-4-4-4440000400000000-444-4-44-400000000000022−220022−2200000022−22−2222000022−22−222200000000000000000000000000000000000000000000
χ8844-4-4-4-4440000400000000-444-4-44-4000000000000−222200−2222000000−222222−220000−222222−2200000000000000000000000000000000000000000000
χ8944-4-4-4-4440000-2000000002-2-222-2223−2323−23−2323−2323000022−220022−22000000−222−2−666−6−222−2−666−60000000000000000000000000000000000000000
χ9044-4-4-4-4440000-2000000002-2-222-2223−2323−23−2323−23230000−222200−22220000002−2−226−6−662−2−226−6−660000000000000000000000000000000000000000
χ9144-4-4-4-4440000-2000000002-2-222-22−2323−232323−2323−23000022−220022−22000000−222−26−6−66−222−26−6−660000000000000000000000000000000000000000
χ9244-4-4-4-4440000-2000000002-2-222-22−2323−232323−2323−230000−222200−22220000002−2−22−666−62−2−22−666−60000000000000000000000000000000000000000
χ934-444-4-44-40000400000000-44-444-4-4000000000000−2i22i2002i2−2i2000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ944-444-4-44-40000400000000-44-444-4-40000000000002i2−2i200−2i22i20000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ954-444-4-44-40000-2000000002-22-2-22223−23−2323−232323−230000−2i22i2002i2−2i2000000i2−i2−i2i2i6−i6−i6i6−i2i2i2−i2−i6i6i6−i60000000000000000000000000000000000000000
χ964-444-4-44-40000-2000000002-22-2-22223−23−2323−232323−2300002i2−2i200−2i22i2000000−i2i2i2−i2−i6i6i6−i6i2−i2−i2i2i6−i6−i6i60000000000000000000000000000000000000000
χ974-444-4-44-40000-2000000002-22-2-222−232323−2323−23−23230000−2i22i2002i2−2i2000000i2−i2−i2i2−i6i6i6−i6−i2i2i2−i2i6−i6−i6i60000000000000000000000000000000000000000
χ984-444-4-44-40000-2000000002-22-2-222−232323−2323−23−232300002i2−2i200−2i22i2000000−i2i2i2−i2i6−i6−i6i6i2−i2−i2i2−i6i6i6−i60000000000000000000000000000000000000000
χ994-44-4-44-4400004000000004-4-44-44-40000000000000022−2200−22220000000022−2222−220000−2222−22220000000000000000000000000000000000000000
χ1004-44-4-44-4400004000000004-4-44-44-400000000000000−22220022−2200000000−2222−2222000022−2222−220000000000000000000000000000000000000000
χ1014-44-4-44-440000-200000000-222-22-2223−23−232323−23−232300000022−2200−22220000−66−66−22−226−66−62−22−20000000000000000000000000000000000000000
χ1024-44-4-44-440000-200000000-222-22-2223−23−232323−23−2323000000−22220022−2200006−66−62−22−2−66−66−22−220000000000000000000000000000000000000000
χ1034-44-4-44-440000-200000000-222-22-22−232323−23−232323−2300000022−2200−222200006−66−6−22−22−66−662−22−20000000000000000000000000000000000000000
χ1044-44-4-44-440000-200000000-222-22-22−232323−23−232323−23000000−22220022−220000−66−662−22−26−66−6−22−220000000000000000000000000000000000000000
χ1054-4-444-4-444-4-44-24-44-4-4-4442222-2-2-2-2-22222-2-2-222-200000000-222-200000000000000000000000000000000000000000000000000000000
χ1064-4-444-4-44-444-4-24-4-4-444-442222-2-2-222-2-2-2-2222-2-2200000000-222-200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4444-444-4-4-2-4-4-444-444-2-22222-222-2-222-2-2-2-2220000000022-2-200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4444-4-4-444-2-4-444-44-44-2-22222-2-2-222-2-22222-2-20000000022-2-200000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).