C₁₀₁×#3020 #27168374

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₀₁×#3020

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 212 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 — 4 generators on 133 points:

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

Conjugacy classes & character table

2929 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#23874, C₁₀₁×#23875, C₁₀₁×#23893, …
maximal normal subgroup of	C₁₀₁×#23874, C₁₀₁×#23875, C₁₀₁×#23893, …
maximal quotient of	C₁₀₁×#18134, C₁₀₁×#18139, C₁₀₁×#18142, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1752);