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C₂×C₂₅×C₁₃⋊C₉ #19154289

order	5850
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₅×C₁₃⋊C₉
unambiguous semidirect product	(C₂×C₁₃)⋊(C₉×C₂₅)
unambiguous semidirect product	(C₂×C₁₃×C₂₅)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₂₅
Hall	C₂×C₁₃×C₂₅ ⋊ C₉
Hall	C₁₃×C₂₅ ⋊ C₂×C₉
Hall	C₂×C₁₃ ⋊ C₉×C₂₅

Subgroups

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

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₅×Dic₁₃⋊C₉, Dic₂₅×C₁₃⋊C₉, Dic₃₂₅⋊C₉, …
maximal normal subgroup of	C₂₅×Dic₁₃⋊C₉, Dic₂₅×C₁₃⋊C₉, Dic₃₂₅⋊C₉, …
maximal quotient of	C₄×C₂₅×C₁₃⋊C₉, C₂²×C₂₅×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 5);