Finite Group Databasebeta

← Prev (#24924470) Next (#24924472) →

C₉×C₂₃×Dic₁₃ #24924471

order	10764
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₂₃×Dic₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₃	D₁₃
commutator, hypocenter	C₁₃	C₄×C₉×C₂₃
Frattini	C₂×C₃	C₃×C₂₃×D₁₃
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle, prime radical	C₂×C₃×C₁₃×C₂₃	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₂₃

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 7);