#45659443

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

Aliases

No aliases for this group.

Splittings

derived, Hall	C₅²×C₇₃ ⋊ C₂×C₉
Hall	C₅²⋊#10620321 ⋊ C₂
Hall	C₅⋊D₃₆₅ ⋊ C₉
Sylow	C₇₃ ⋊ (C₅⋊D₅)⋊C₉
Sylow	C₅² ⋊ #10620321⋊C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	#24926546
commutator, hypocenter	C₅²×C₇₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₅²×C₇₃	C₂×C₃
prime radical	C₃×C₅⋊D₃₆₅	C₃
LCS	G ▷ C₅²×C₇₃
UCS	C₁ ◁ C₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 3285

A minimal faithful permutation representation — 2 generators on 97 points:

(1,2,4)(3,13,9,6,7,15)(5,10,14,11,12,8)(16,20,24,18,23,19,21,17,22)(26,30,31,27,28,32)(29,38,39,33,34,48)(35,51,52,41,42,65)(36,50,46,44,40,37)(43,70,71,54,55,84)(45,68,69,57,53,62)(47,49,67,59,60,63)(56,72,81,58,73,87)(61,66,86,74,75,82)(64,91,89,78,79,77)(76,85,92,80,88,96)(83,97,95,93,94,90);(1,3,8,14,6)(2,5,7,13,11)(4,9,10,12,15)(25,26,29,35,43,56,57,44,28,32,37,47,61,76,78,60,34,40,48,62,77,90,93,75,42,53,63,65,81,92,97,88,55,72,79,82,84,71,86,91,73,70,85,94,96,87,52,67,68,51,66,83,95,89,69,39,50,38,49,64,80,74,59,46,31,30,36,45,58,54,41,33,27)

Polycyclic presentation:

2,3,5^2,73,3|b^3=f,c^a=c^4,d^a=d^4,e^a=e^72,c^b=cd,d^b=c^2d^3,e^b=e^8

Conjugacy classes & character table

930 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32850, 46);