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C₄×C₇⋊C₉×C₈₉ #36375820

order	22428
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₇⋊C₉×C₈₉
unambiguous semidirect product	(C₄×C₇)⋊(C₉×C₈₉)
unambiguous semidirect product	(C₄×C₇×C₈₉)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₄×C₉×C₈₉
Hall	C₄×C₇×C₈₉ ⋊ C₉
Hall	C₇×C₈₉ ⋊ C₄×C₉
Hall	C₄×C₇ ⋊ C₉×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₈₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₄×C₉×C₈₉
Frattini	C₂×C₃	C₂×ΓL(1,𝔽₈)×C₈₉
Fitting	C₃×C₄×C₇×C₈₉	C₃
socle, prime radical	C₂×C₃×C₇×C₈₉	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₈₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄×C₈₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22428

Conjugacy classes & character table

5340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22428, 2);