Finite Group Databasebeta

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C₂₃×Dic₁₁₇ #24924475

order	10764
isoclinism	isoclinic class of D₁₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×Dic₁₁₇
unambiguous semidirect product	C₉⋊(C₂₃×Dic₁₃)

Splittings

derived, Hall	C₉×C₁₃ ⋊ C₄×C₂₃
Hall	C₉×C₁₃×C₂₃ ⋊ C₄
Hall	C₁₃×C₂₃ ⋊ Dic₉
Hall	C₉×C₂₃ ⋊ Dic₁₃
Sylow	C₁₃ ⋊ C₂₃×Dic₉
Sylow	C₉ ⋊ C₂₃×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₁₁₇
commutator, hypocenter	C₉×C₁₃	C₄×C₂₃
Frattini	C₂×C₃	C₂₃×D₃₉
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle, prime radical	C₂×C₃×C₁₃×C₂₃	D₃
cosocle	C₂×C₉×C₁₃	C₂×C₂₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂×C₂₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 11);