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C₂₃×D₇₉⋊C₉ #45658407

order	32706
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×D₇₉⋊C₉
unambiguous semidirect product	D₇₉⋊(C₉×C₂₃)
unambiguous semidirect product	(C₇₉⋊C₉)⋊(C₂×C₂₃)
unambiguous semidirect product	(C₂₃×D₇₉)⋊C₉

Splittings

derived, Sylow	C₇₉ ⋊ C₂×C₉×C₂₃
Hall	C₂₃×C₇₉⋊C₉ ⋊ C₂
Hall	C₂₃×D₇₉ ⋊ C₉
Hall	C₂₃×C₇₉ ⋊ C₂×C₉
Hall	C₇₉⋊C₉ ⋊ C₂×C₂₃
Hall	D₇₉ ⋊ C₉×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₇₉⋊C₃
commutator, hypocenter	C₇₉	C₂×C₉×C₂₃
Frattini	C₃	C₂₃×D₇₉⋊C₃
Fitting, socle	C₃×C₂₃×C₇₉	C₂×C₃
prime radical	C₃×C₂₃×D₇₉	C₃
cosocle	C₃×C₇₉	C₂×C₃×C₂₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16353

Conjugacy classes & character table

1311 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32706, 10);