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C₂⁴×C₄×C₇×C₂₃ #72188947

order	10304
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1362493440
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁴×C₄×C₇×C₂₃
multiplicative	(ℤ/32712)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁵×C₇×C₂₃
socle, prime radical	C₂⁵×C₇×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

2724 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10304 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₇×C₈×C₂₃, C₂³×C₄²×C₇×C₂₃, C₂⁵×C₄×C₇×C₂₃, …
maximal normal subgroup of	C₂⁴×C₇×C₈×C₂₃, C₂³×C₄²×C₇×C₂₃, C₂⁵×C₄×C₇×C₂₃, …
maximal quotient of	C₂⁴×C₇×C₈×C₂₃, C₂³×C₄²×C₇×C₂₃, C₂⁵×C₄×C₇×C₂₃, …
automorphism group of	C₃×C₈×C₂₉×C₄₇
outer automorphism group of	C₃×C₈×C₂₉×C₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.