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C₁₇×C₆₇⋊C₉ #23779598

order	10251
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₆₇⋊C₉
unambiguous semidirect product	C₆₇⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₇×C₆₇)⋊C₉

Splittings

derived, Sylow	C₆₇ ⋊ C₉×C₁₇
Hall	C₁₇×C₆₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₆₇⋊C₃
commutator, hypocenter	C₆₇	C₉×C₁₇
Frattini	C₃	C₁₇×C₆₇⋊C₃
Fitting, socle, prime radical	C₃×C₁₇×C₆₇	C₃
cosocle	C₃×C₆₇	C₃×C₁₇
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₃×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₇×C₆₇⋊C₉, C₁₇×D₆₇⋊C₉, D₁₇×C₆₇⋊C₉, …
maximal normal subgroup of	C₂×C₁₇×C₆₇⋊C₉, C₁₇×D₆₇⋊C₉, D₁₇×C₆₇⋊C₉, …
maximal quotient of	C₂×C₁₇×C₆₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10251, 2);