C₁₀₁×#2192 #27167546

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₁×#2192

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂×C₄×C₁₀₁ ◁ #131×C₁₀₁ ◁ G

220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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)(3,14)(4,18)(5,12)(6,11)(7,13)(8,15)(9,16)(10,21)(17,29)(19,30)(20,24)(22,28)(23,27)(25,32)(26,31)(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)(2,8)(4,19)(5,16)(6,23)(7,17)(9,24)(10,27)(11,25)(12,30)(13,26)(14,18)(15,21)(20,31)(22,32)(28,29);(1,3)(2,9)(4,15)(5,23)(6,16)(7,17)(8,24)(10,26)(11,29)(12,14)(13,27)(18,30)(19,21)(20,32)(22,31)(25,28)

Conjugacy classes & character table

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

Relationships

maximal quotient of

C₁₀₁×#12108, C₁₀₁×#12110, C₁₀₁×#12164, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 924);