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C₂×C₁₇⋊#64418 #23756229

order	9996
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₇⋊#64418
unambiguous semidirect product	(C₂×C₁₇)⋊#64418

Splittings

Fitting, socle	C₂×C₇²×C₁₇ ⋊ D₃
derived, Hall	C₁₇×#3862 ⋊ C₂²
Hall	C₇²×C₁₇ ⋊ C₂×D₃
Hall	#3862 ⋊ C₂×D₁₇
Sylow	C₇² ⋊ C₂×D₅₁
Sylow	C₁₇ ⋊ C₂×#64418

Subgroups

	subgroup	G/H
center, hypercenter	C₂	C₁₇⋊#64418
commutator, cosocle, hypocenter	C₁₇×#3862	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₇	D₃
LCS	G ▷ C₁₇×#3862
UCS	C₁ ◁ C₂

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

344 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₇⋊(#64418⋊C₃), D₃×C₁₇⋊#64418, C₂×C₃×C₁₇⋊#64418, …
maximal normal subgroup of	C₂×C₁₇⋊(#64418⋊C₃), C₂×C₃×C₁₇⋊#64418
maximal quotient of	C₂×C₁₇⋊#11725071, D₃×C₁₇⋊#64418, C₂×C₃×C₁₇⋊#64418, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 132);