M₃₂×C₆₇ #14523914

order	2144
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

M₃₂×C₆₇

Subgroups

	subgroup	G/H
center	C₈×C₆₇	C₂²
commutator	C₂	C₂×C₈×C₆₇
Frattini, cosocle	C₈	C₂²×C₆₇
socle	C₂×C₆₇	C₂×C₈
prime radical	C₂²×C₆₇	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₆₇ ◁ G

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 1072

A minimal faithful permutation representation — 2 generators on 83 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);(2,10)(4,12)(6,14)(8,16)

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#16863173, #16863177, #16863181, …
maximal subgroup of	#347×C₆₇, #349×C₆₇, #350×C₆₇, …
maximal normal subgroup of	#347×C₆₇, #349×C₆₇, #350×C₆₇, …
maximal quotient of	#346×C₆₇, C₂²⋊C₁₆×C₆₇, C₄⋊C₁₆×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2144, 17);

M32×C67 #14523914