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C₂×C₇⋊C₉×C₇₁ #22582113

order	8946
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇⋊C₉×C₇₁
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₇₁)
unambiguous semidirect product	(C₂×C₇×C₇₁)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₇₁
Hall	C₂×C₇×C₇₁ ⋊ C₉
Hall	C₇×C₇₁ ⋊ C₂×C₉
Hall	C₂×C₇ ⋊ C₉×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇₁	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₇₁
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₇₁
Fitting, socle	C₂×C₃×C₇×C₇₁	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₇₁

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2130 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇⋊C₉×C₇₁, C₇⋊C₉×Dic₇₁, C₇₁×Dic₇⋊C₉, …
maximal normal subgroup of	C₄×C₇⋊C₉×C₇₁, C₇⋊C₉×Dic₇₁, C₇₁×Dic₇⋊C₉, …
maximal quotient of	C₄×C₇⋊C₉×C₇₁, C₂²×C₇⋊C₉×C₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8946, 3);