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D₇×C₂₅×C₈₉ #44528263

order	31150
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₂₅×C₈₉
unambiguous semidirect product	C₇⋊(C₂×C₂₅×C₈₉)

Splittings

Fitting, Hall	C₇×C₂₅×C₈₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₂₅×C₈₉
Hall	C₇×C₈₉ ⋊ C₂×C₂₅
Hall	C₇×C₂₅ ⋊ C₂×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅×C₈₉	D₇
commutator, hypocenter	C₇	C₂×C₂₅×C₈₉
Frattini	C₅	C₅×D₇×C₈₉
Fitting	C₇×C₂₅×C₈₉	C₂
socle	C₅×C₇×C₈₉	C₂×C₅
prime radical	C₅×D₇×C₈₉	C₅
cosocle	C₅×C₇	C₂×C₅×C₈₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂₅×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15575

Conjugacy classes & character table

11125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31150, 3);