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C₁₉×Dic₂₂₅ #30685374

order	17100
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₂₂₅
unambiguous semidirect product	C₉⋊(C₁₉×Dic₂₅)

Splittings

derived, Hall	C₉×C₂₅ ⋊ C₄×C₁₉
Hall	C₉×C₁₉×C₂₅ ⋊ C₄
Hall	C₁₉×C₂₅ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ Dic₂₅
Sylow	C₂₅ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×Dic₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₂₅
commutator, hypocenter	C₉×C₂₅	C₄×C₁₉
Frattini	C₂×C₃×C₅	C₁₉×D₁₅
Fitting	C₂×C₉×C₁₉×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅×C₁₉	D₁₅
cosocle	C₂×C₉×C₂₅	C₂×C₁₉
LCS	G ▷ C₉×C₂₅
UCS	C₁ ◁ C₂×C₁₉

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17100

Conjugacy classes & character table

4332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 11);