Finite Group Databasebeta

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Dic₂₅×C₃₁⋊C₉ #42124261

order	27900
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₂₅×C₃₁⋊C₉
unambiguous semidirect product	(C₃₁×Dic₂₅)⋊C₉

Splittings

derived, Hall	C₂₅×C₃₁ ⋊ C₄×C₉
Hall	C₂₅×C₃₁⋊C₉ ⋊ C₄
Hall	C₃₁×Dic₂₅ ⋊ C₉
Sylow	C₃₁ ⋊ C₉×Dic₂₅
Sylow	C₂₅ ⋊ C₄×C₃₁⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₅×C₃₁⋊C₃
commutator, hypocenter	C₂₅×C₃₁	C₄×C₉
Frattini	C₂×C₃×C₅	D₅×C₃₁⋊C₃
Fitting, cosocle	C₂×C₃×C₂₅×C₃₁	C₂×C₃
socle, prime radical	C₂×C₃×C₅×C₃₁	C₃×D₅
LCS	G ▷ C₂₅×C₃₁
UCS	C₁ ◁ C₂×C₃

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 8);