C₁₀₉×#2063 #28359317

order	13952
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₉×#2063

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₉
prime radical	C₂²×D₄×C₁₀₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂²×C₄×C₁₀₉ ◁ G

228 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 129
transitive degree	μ_t(G) = 3488

A minimal faithful permutation representation — 3 generators on 129 points:

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

Conjugacy classes & character table

2834 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₉×#2063, C₁₀₉×#23601, C₁₀₉×#23602, …
maximal normal subgroup of	C₂×C₁₀₉×#2063, C₁₀₉×#23601, C₁₀₉×#23602, …
maximal quotient of	C₁₀₉×#10587, C₁₀₉×#10589, C₁₀₉×#10591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 795);