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C₄²×C₈×C₉² #72189012

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 382205952
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³×C₉

Aliases

abelian	C₄²×C₈×C₉²
multiplicative	(ℤ/13505)ˣ, (ℤ/27010)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃²×C₄	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂²×C₃²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

4692 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄²×C₉²×C₁₆, C₄×C₈²×C₉², C₂×C₄²×C₈×C₉², …
maximal normal subgroup of	C₄²×C₉²×C₁₆, C₄×C₈²×C₉², C₂×C₄²×C₈×C₉², …
maximal quotient of	C₄²×C₉²×C₁₆, C₄×C₈²×C₉², C₂×C₄²×C₈×C₉², …
automorphism group of	C₅×C₃₇×C₇₃
outer automorphism group of	C₅×C₃₇×C₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.