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C₃⋊D₃×C₂₅×C₇₉ #48001190

order	35550
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅×C₇₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊D₃×C₂₅×C₇₉
unambiguous semidirect product	C₃⋊(D₃×C₂₅×C₇₉)

Splittings

Fitting, Hall	C₃²×C₂₅×C₇₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₂₅×C₇₉
Hall	C₃²×C₇₉ ⋊ C₂×C₂₅
Hall	C₃²×C₂₅ ⋊ C₂×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅×C₇₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₂₅×C₇₉
Frattini	C₅	C₅×C₃⋊D₃×C₇₉
Fitting	C₃²×C₂₅×C₇₉	C₂
socle	C₃²×C₅×C₇₉	C₂×C₅
prime radical	C₅×C₃⋊D₃×C₇₉	C₅
cosocle	C₃²×C₅	C₂×C₅×C₇₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₅×C₇₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17775

Conjugacy classes & character table

11850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35550, 29);