Finite Group Databasebeta

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C₂×C₉×C₂₃×C₂₇ #72189665

order	11178
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 192456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉

Aliases

C₂×C₉×C₂₃×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₉	C₂×C₃²×C₂₃
socle, prime radical	C₂×C₃²×C₂₃	C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₉×C₂₃×C₂₇, C₂²×C₉×C₂₃×C₂₇
maximal normal subgroup of	C₄×C₉×C₂₃×C₂₇, C₂²×C₉×C₂₃×C₂₇
maximal quotient of	C₄×C₉×C₂₃×C₂₇, C₂²×C₉×C₂₃×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.