C₃×#24926548 #45659486

order	32850
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product

C₃×#24926548

Splittings

Fitting, socle	C₃×C₅²×C₇₃ ⋊ C₂×C₃
derived, Hall	C₅²×C₇₃ ⋊ C₂×C₃²
Hall	C₃×C₇₃×C₅²⋊C₃ ⋊ C₂
Hall	C₅⋊D₃₆₅ ⋊ C₃²
Hall	C₃×C₅²⋊C₃ ⋊ D₇₃
Sylow	C₇₃ ⋊ C₃×(C₅⋊D₅)⋊C₃
Sylow	C₅² ⋊ C₃²×D₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	#24926548
commutator, cosocle, hypocenter	C₅²×C₇₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇₃	C₂×C₃
LCS	G ▷ C₅²×C₇₃
UCS	C₁ ◁ C₃

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 3285

A minimal faithful permutation representation — 2 generators on 91 points:

(4,5,7)(6,16,12,9,10,18)(8,13,17,14,15,11)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91);(1,2,3)(4,6,11,17,9)(5,8,10,16,14)(7,12,13,15,18)(19,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21)

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32850, 89);

C3×#24926548 #45659486