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C₂×C₁₉×C₃₁⋊C₂₅ #44441284

order	29450
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₃₁⋊C₂₅
unambiguous semidirect product	(C₂×C₃₁)⋊(C₁₉×C₂₅)
unambiguous semidirect product	(C₂×C₁₉×C₃₁)⋊C₂₅

Splittings

derived, Sylow	C₃₁ ⋊ C₂×C₁₉×C₂₅
Hall	C₂×C₁₉×C₃₁ ⋊ C₂₅
Hall	C₁₉×C₃₁ ⋊ C₂×C₂₅
Hall	C₂×C₃₁ ⋊ C₁₉×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃₁	C₂×C₁₉×C₂₅
Frattini	C₅	C₂×C₁₉×ΓL(1,𝔽₃₂)
Fitting, socle, prime radical	C₂×C₅×C₁₉×C₃₁	C₅
cosocle	C₅×C₃₁	C₂×C₅×C₁₉
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₅×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 29450

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29450, 2);