#46777413

order	33620
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Sylow	C₄₁² ⋊ C₄×C₅
Hall	C₄₁×C₄₁⋊C₅ ⋊ C₄
Hall	#20269609 ⋊ C₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₄₁²	C₄×C₅
prime radical	(C₄₁⋊C₅)⋊D₄₁	C₂
cosocle	C₄₁⋊D₄₁	C₂×C₅
LCS	G ▷ C₄₁²
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 410

A minimal faithful permutation representation — 2 generators on 82 points:

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

Polycyclic presentation:

2,5,2,41^2|a^2=c,d^a=d^32,e^a=e^9,d^b=d^10,d^c=d^40,e^c=e^40

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33620, 48);