Finite Group Databasebeta

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C₂×C₈×C₉×C₇₉ #72189863

order	11376
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7488
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₈×C₉×C₇₉
multiplicative	(ℤ/17067)ˣ, (ℤ/22756)ˣ, (ℤ/34134)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃×C₇₉
socle, prime radical	C₂²×C₃×C₇₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11376 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₉×C₁₆×C₇₉, C₄×C₈×C₉×C₇₉, C₂²×C₈×C₉×C₇₉
maximal normal subgroup of	C₂×C₉×C₁₆×C₇₉, C₄×C₈×C₉×C₇₉, C₂²×C₈×C₉×C₇₉
maximal quotient of	C₂×C₉×C₁₆×C₇₉, C₄×C₈×C₉×C₇₉, C₂²×C₈×C₉×C₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.