C₁₀₁×#2212 #27167566

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₁×#2212

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
prime radical	#509×C₁₀₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂×C₄×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

154 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 3232

A minimal faithful permutation representation — 3 generators on 133 points:

(1,2)(3,13)(4,16)(5,21)(6,8)(7,12)(9,18)(10,22)(11,15)(14,28)(17,29)(19,30)(20,32)(23,26)(24,25)(27,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133);(1,3,5,6,7,15,22,24)(2,8,10,13,12,25,21,11)(4,14,17,23,20,18,19,31)(9,16,26,30,28,32,27,29);(1,4)(2,9)(3,14)(5,17)(6,23)(7,20)(8,16)(10,26)(11,29)(12,28)(13,30)(15,18)(19,22)(21,27)(24,31)(25,32)

Conjugacy classes & character table

2323 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient of

C₁₀₁×#12416, C₁₀₁×#12417, C₁₀₁×#12420, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 944);