C₁₀₁×#1763 #27167117

order	12928
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₀₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₀₁×#1763

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₁	C₂×D₄
commutator	C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

324 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 117
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 3 generators on 117 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#8417, C₁₀₁×#8419, C₁₀₁×#9164, …
maximal normal subgroup of	C₁₀₁×#8417, C₁₀₁×#8419, C₁₀₁×#9164, …
maximal quotient of	C₁₀₁×#8171, C₁₀₁×#8173, C₁₀₁×#8178, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 495);