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C₂×D₁₇×C₁₃⋊C₉ #22547351

order	7956
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₁₇×C₁₃⋊C₉
unambiguous semidirect product	C₁₇⋊(C₂²×C₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₂×C₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₁₃×D₁₇)⋊C₉

Splittings

derived, Hall	C₁₃×C₁₇ ⋊ C₂²×C₉
Hall	C₁₇×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×C₁₃×D₁₇ ⋊ C₉
Sylow	C₁₇ ⋊ C₂²×C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×C₉×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₇×C₁₃⋊C₃
commutator, hypocenter	C₁₃×C₁₇	C₂²×C₉
Frattini	C₃	C₂×D₁₇×C₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 23);