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C₂⁵×C₃²×C₂₃ #72185758

order	6624
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10559324160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

abelian	C₂⁵×C₃²×C₂₃
multiplicative	(ℤ/23352)ˣ, (ℤ/23688)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

4488 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃²×C₄×C₂₃, C₂⁶×C₃²×C₂₃, C₂⁵×C₃×C₉×C₂₃, …
maximal normal subgroup of	C₂⁴×C₃²×C₄×C₂₃, C₂⁶×C₃²×C₂₃, C₂⁵×C₃×C₉×C₂₃, …
maximal quotient of	C₂⁴×C₃²×C₄×C₂₃, C₂⁶×C₃²×C₂₃, C₂⁵×C₃×C₉×C₂₃, …
automorphism group of	C₃×C₇×C₈×C₁₃₉, C₇×C₈×C₉×C₄₇
outer automorphism group of	C₃×C₇×C₈×C₁₃₉, C₇×C₈×C₉×C₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.