C₁₀₇×#1969 #28332652

order	13696
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₀₇×#1969

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ C₂×C₄²×C₁₀₇ ◁ G

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

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 131
transitive degree	μ_t(G) = 13696

A minimal faithful permutation representation — 3 generators on 131 points:

(2,4)(5,6,7,8)(9,10)(11,16)(12,21)(13,23)(14,18)(15,19)(17,22)(20,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(1,2,3,4)(6,8)(9,11,13,19,14,20,22,12)(10,15,17,16,18,21,23,24);(9,12,22,20,14,19,13,11)(10,16,23,15,18,24,17,21)

Conjugacy classes & character table

4708 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#7113, C₁₀₇×#13014, C₁₀₇×#13015, …
maximal normal subgroup of	C₁₀₇×#7113, C₁₀₇×#13014, C₁₀₇×#13015, …
maximal quotient of	C₁₀₇×#9656, C₁₀₇×#9662, C₁₀₇×#9718, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 701);