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C₁₉×Dic₁₅₃ #26042563

order	11628
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₁₅₃
unambiguous semidirect product	C₉⋊(C₁₉×Dic₁₇)

Splittings

derived, Hall	C₉×C₁₇ ⋊ C₄×C₁₉
Hall	C₉×C₁₇×C₁₉ ⋊ C₄
Hall	C₁₇×C₁₉ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ Dic₁₇
Sylow	C₁₇ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×Dic₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₁₅₃
commutator, hypocenter	C₉×C₁₇	C₄×C₁₉
Frattini	C₂×C₃	C₁₉×D₅₁
Fitting	C₂×C₉×C₁₇×C₁₉	C₂
socle, prime radical	C₂×C₃×C₁₇×C₁₉	D₃
cosocle	C₂×C₉×C₁₇	C₂×C₁₉
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ C₂×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11628, 11);