C₁₀₁×#2250 #27167604

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₁×#2250

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

198 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 121
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 3 generators on 121 points:

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

Conjugacy classes & character table

2626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#12324, C₁₀₁×#12325, C₁₀₁×#12336, …
maximal normal subgroup of	C₁₀₁×#12324, C₁₀₁×#12325, C₁₀₁×#12336, …
maximal quotient of	C₁₀₁×#12506, C₁₀₁×#12508, C₁₀₁×#12512, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 982);