Finite Group Databasebeta

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C₁₉×C₂₅×C₇⋊C₉ #44471673

order	29925
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₂₅×C₇⋊C₉
unambiguous semidirect product	C₇⋊(C₉×C₁₉×C₂₅)
unambiguous semidirect product	(C₇×C₂₅)⋊(C₉×C₁₉)

Splittings

derived, Sylow	C₇ ⋊ C₉×C₁₉×C₂₅
Hall	C₇×C₁₉×C₂₅ ⋊ C₉
Hall	C₇×C₂₅ ⋊ C₉×C₁₉
Hall	C₇×C₁₉ ⋊ C₉×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉×C₂₅	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₉×C₂₅
Frattini	C₃×C₅	C₅×C₁₉×ΓL(1,𝔽₈)
Fitting	C₃×C₇×C₁₉×C₂₅	C₃
socle, prime radical	C₃×C₅×C₇×C₁₉	C₃×C₅
cosocle	C₃×C₅×C₇	C₃×C₅×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₉×C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 29925

Conjugacy classes & character table

7125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29925, 3);