D₃×C₅²⋊(C₇₃⋊C₃) #45659494

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

Aliases

direct product	D₃×C₅²⋊(C₇₃⋊C₃)
unambiguous semidirect product	C₃⋊(C₂×C₅²⋊(C₇₃⋊C₃))
unambiguous semidirect product	(C₅²×D₃)⋊(C₇₃⋊C₃)
unambiguous semidirect product	(D₃×C₇₃)⋊(C₅²⋊C₃)

Splittings

Fitting, socle, derived	C₃×C₅²×C₇₃ ⋊ C₂×C₃
Hall	C₃×C₅²⋊(C₇₃⋊C₃) ⋊ C₂
Hall	C₅²×C₇₃ ⋊ C₃×D₃
Sylow	C₇₃ ⋊ D₃×C₅²⋊C₃
Sylow	C₅² ⋊ D₃×C₇₃⋊C₃

Subgroups

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

52 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:

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

Conjugacy classes & character table

1833 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32850, 97);

D3×C52⋊(C73⋊C3) #45659494