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C₂×C₄₇×C₇⋊C₉ #20238352

order	5922
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₄₇×C₇⋊C₉
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₄₇)
unambiguous semidirect product	(C₂×C₇×C₄₇)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₄₇
Hall	C₂×C₇×C₄₇ ⋊ C₉
Hall	C₇×C₄₇ ⋊ C₂×C₉
Hall	C₂×C₇ ⋊ C₉×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₄₇
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₄₇
Fitting, socle	C₂×C₃×C₇×C₄₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₄₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇⋊C₉×Dic₄₇, C₄₇×Dic₇⋊C₉, C₄₇⋊(Dic₇⋊C₉), …
maximal normal subgroup of	C₇⋊C₉×Dic₄₇, C₄₇×Dic₇⋊C₉, C₄₇⋊(Dic₇⋊C₉), …
maximal quotient of	C₄×C₄₇×C₇⋊C₉, C₂²×C₄₇×C₇⋊C₉, C₂×C₅×C₄₇×C₇⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5922, 5);