C₁₀₁×#2399 #27167753

order	12928
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₁×#2399

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₀₁
socle, prime radical	C₂³×C₁₀₁	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

504 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 12928

A minimal faithful permutation representation — 4 generators on 121 points:

(5,6)(7,10)(8,9)(11,12)(13,14,17,20)(15,19,16,18)(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);(1,2)(3,4)(13,15,17,16)(14,18,20,19);(2,4)(6,9)(10,12)(13,15,17,16)(14,19,20,18);(5,7,8,11)(6,10,9,12)(13,16,17,15)(14,18,20,19)

Conjugacy classes & character table

4444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#9030, C₁₀₁×#10014, C₁₀₁×#10017, …
maximal normal subgroup of	C₁₀₁×#9030, C₁₀₁×#10014, C₁₀₁×#10017, …
maximal quotient of	C₁₀₁×#13848, C₁₀₁×#13850, C₁₀₁×#13856, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1131);