M₃₂×C₈₃ #14581663

order	2656
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

M₃₂×C₈₃

Subgroups

	subgroup	G/H
center	C₈×C₈₃	C₂²
commutator	C₂	C₂×C₈×C₈₃
Frattini, cosocle	C₈	C₂²×C₈₃
socle	C₂×C₈₃	C₂×C₈
prime radical	C₂²×C₈₃	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₈₃ ◁ G

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 99
transitive degree	μ_t(G) = 1328

A minimal faithful permutation representation — 2 generators on 99 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,10)(4,12)(6,14)(8,16)

Conjugacy classes & character table

1660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#347×C₈₃, #349×C₈₃, #350×C₈₃, …
maximal normal subgroup of	#347×C₈₃, #349×C₈₃, #350×C₈₃, …
maximal quotient of	#346×C₈₃, C₂²⋊C₁₆×C₈₃, C₄⋊C₁₆×C₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2656, 17);

M32×C83 #14581663