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C₄²×C₉×C₇₉ #72189865

order	11376
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 44928
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₉×C₇₉
multiplicative	(ℤ/11729)ˣ, (ℤ/23458)ˣ

Subgroups

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

90 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	C₄×C₈×C₉×C₇₉, C₂×C₄²×C₉×C₇₉
maximal normal subgroup of	C₄×C₈×C₉×C₇₉, C₂×C₄²×C₉×C₇₉
maximal quotient of	C₄×C₈×C₉×C₇₉, C₂×C₄²×C₉×C₇₉
automorphism group of	C₃₇×C₃₁₇
outer automorphism group of	C₃₇×C₃₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.