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C₇₃×(C₅⋊D₅)⋊C₉ #45659442

order	32850
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₇₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₇₃×(C₅⋊D₅)⋊C₉
unambiguous semidirect product	(C₅⋊D₅)⋊(C₉×C₇₃)

Splittings

derived, Sylow	C₅² ⋊ C₂×C₉×C₇₃
Hall	C₇₃×C₅²⋊C₉ ⋊ C₂
Hall	C₅⋊D₅×C₇₃ ⋊ C₉
Hall	C₅²×C₇₃ ⋊ C₂×C₉
Hall	C₅²⋊C₉ ⋊ C₂×C₇₃
Hall	C₅⋊D₅ ⋊ C₉×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₃	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₂×C₉×C₇₃
Frattini	C₃	C₇₃×(C₅⋊D₅)⋊C₃
Fitting, socle	C₃×C₅²×C₇₃	C₂×C₃
prime radical	C₃×C₅⋊D₅×C₇₃	C₃
cosocle	C₃×C₅²	C₂×C₃×C₇₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₇₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3285

Conjugacy classes & character table

2190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32850, 45);