M₃₂×C₁₀₁ #15692126

order	3232
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₀₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

M₃₂×C₁₀₁

Subgroups

	subgroup	G/H
center	C₈×C₁₀₁	C₂²
commutator	C₂	C₂×C₈×C₁₀₁
Frattini, cosocle	C₈	C₂²×C₁₀₁
socle	C₂×C₁₀₁	C₂×C₈
prime radical	C₂²×C₁₀₁	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₀₁ ◁ G

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 2 generators on 117 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(2,10)(4,12)(6,14)(8,16)

Conjugacy classes & character table

2020 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#347×C₁₀₁, #349×C₁₀₁, #350×C₁₀₁, …
maximal normal subgroup of	#347×C₁₀₁, #349×C₁₀₁, #350×C₁₀₁, …
maximal quotient of	#346×C₁₀₁, C₂²⋊C₁₆×C₁₀₁, C₄⋊C₁₆×C₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 17);

M32×C101 #15692126