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Dic₂₅×C₁₃⋊C₉ #26043156

order	11700
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₂₅×C₁₃⋊C₉
unambiguous semidirect product	(C₁₃×Dic₂₅)⋊C₉

Splittings

derived, Hall	C₁₃×C₂₅ ⋊ C₄×C₉
Hall	C₂₅×C₁₃⋊C₉ ⋊ C₄
Hall	C₁₃×Dic₂₅ ⋊ C₉
Sylow	C₂₅ ⋊ C₄×C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₉×Dic₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊C₃×D₂₅
commutator, hypocenter	C₁₃×C₂₅	C₄×C₉
Frattini	C₂×C₃×C₅	D₅×C₁₃⋊C₃
Fitting, cosocle	C₂×C₃×C₁₃×C₂₅	C₂×C₃
socle, prime radical	C₂×C₃×C₅×C₁₃	C₃×D₅
LCS	G ▷ C₁₃×C₂₅
UCS	C₁ ◁ C₂×C₃

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

588 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 3);