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C₂×C₄×C₉²×C₁₆ #72188997

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 15925248
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄×C₉

Aliases

abelian	C₂×C₄×C₉²×C₁₆
multiplicative	(ℤ/11951)ˣ, (ℤ/16983)ˣ, (ℤ/23902)ˣ, (ℤ/33966)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃²×C₈	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂×C₃²×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

2484 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	C₂×C₄×C₉²×C₃₂, C₂×C₈×C₉²×C₁₆, C₄²×C₉²×C₁₆, …
maximal normal subgroup of	C₂×C₄×C₉²×C₃₂, C₂×C₈×C₉²×C₁₆, C₄²×C₉²×C₁₆, …
maximal quotient of	C₂×C₄×C₉²×C₃₂, C₂×C₈×C₉²×C₁₆, C₄²×C₉²×C₁₆, …
automorphism group of	C₁₇×C₁₉×C₃₇, C₁₇×C₂₇×C₃₇
outer automorphism group of	C₁₇×C₁₉×C₃₇, C₁₇×C₂₇×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.