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C₂×D₁₇×#4294 #26042571

order	11628
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₁₇×#4294
unambiguous semidirect product	C₁₇⋊(C₂²×#4294)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₂×#4294)

Splittings

derived, Hall	C₁₇×C₁₉ ⋊ C₂²×C₉
Hall	C₁₇×#4294 ⋊ C₂²
Hall	C₂×C₁₉×D₁₇ ⋊ C₉
Sylow	C₁₉ ⋊ C₂×C₉×D₁₇
Sylow	C₁₇ ⋊ C₂²×#4294

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₇×C₁₉⋊C₃
commutator, hypocenter	C₁₇×C₁₉	C₂²×C₉
Frattini	C₃	C₂×D₁₇×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₁₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×D₁₇	C₃
cosocle	C₃×C₁₇×C₁₉	C₂²×C₃
LCS	G ▷ C₁₇×C₁₉
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

540 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 19);