C₁₀₇×#1383 #28332066

order	13696
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₇×#1383

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#106
commutator	C₈	C₄²×C₁₀₇
Frattini, cosocle	C₂²×C₈	C₂²×C₁₀₇
prime radical	C₂³×C₁₀₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ C₂²×C₈×C₁₀₇ ◁ G

136 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 127
transitive degree	μ_t(G) = 3424

A minimal faithful permutation representation — 2 generators on 127 points:

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

Conjugacy classes & character table

3424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₇×#1383, C₁₀₇×#12563, C₁₀₇×#12647, …
maximal normal subgroup of	C₂×C₁₀₇×#1383, C₁₀₇×#12563, C₁₀₇×#12647, …
maximal quotient of	C₁₀₇×#7156, C₁₀₇×#7173, C₁₀₇×#7174, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 115);