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C₉×D₁₃×D₁₇ #22547358

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

Aliases

C₉×D₁₃×D₁₇

Splittings

Fitting, Hall	C₉×C₁₃×C₁₇ ⋊ C₂²
derived, Hall	C₁₃×C₁₇ ⋊ C₂²×C₉
Hall	C₉×C₁₇ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₉×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₃×D₁₇
commutator, hypocenter	C₁₃×C₁₇	C₂²×C₉
Frattini	C₃	C₃×D₁₃×D₁₇
Fitting	C₉×C₁₃×C₁₇	C₂²
socle	C₃×C₁₃×C₁₇	C₂²×C₃
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

720 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 30);