C₁₀₇×#2921 #28333604

order	13696
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₀₇×#2921

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₀₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₇
socle	C₂²×C₁₀₇	C₂³×C₄
prime radical	C₂⁴×C₁₀₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₇ ◁ G

392 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 3424

A minimal faithful permutation representation — 4 generators on 131 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₇×#8863, C₁₀₇×#9034, C₁₀₇×#9036, …
maximal normal subgroup of	C₁₀₇×#8863, C₁₀₇×#9034, C₁₀₇×#9036, …
maximal quotient of	C₁₀₇×#20365, C₁₀₇×#20377, C₁₀₇×#20429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 1653);