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C₂×C₄²×C₉×C₂₃ #72185751

order	6624
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 202752
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄²×C₉×C₂₃
multiplicative	(ℤ/8695)ˣ, (ℤ/12435)ˣ, (ℤ/13264)ˣ, (ℤ/16580)ˣ, (ℤ/17390)ˣ, (ℤ/24870)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂³×C₃×C₂₃
socle, prime radical	C₂³×C₃×C₂₃	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 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	C₂×C₄×C₈×C₉×C₂₃, C₄³×C₉×C₂₃, C₂²×C₄²×C₉×C₂₃, …
maximal normal subgroup of	C₂×C₄×C₈×C₉×C₂₃, C₄³×C₉×C₂₃, C₂²×C₄²×C₉×C₂₃, …
maximal quotient of	C₂×C₄×C₈×C₉×C₂₃, C₄³×C₉×C₂₃, C₂²×C₄²×C₉×C₂₃, …
automorphism group of	C₅×C₃₇×C₄₇
outer automorphism group of	C₅×C₃₇×C₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.