C₁₀₇×#1376 #28332059

order	13696
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₀₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₇×#1376

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₀₇	D₄
commutator	C₄	C₄×C₈×C₁₀₇
Frattini, cosocle	C₂²×C₈	C₂²×C₁₀₇
socle	C₂²×C₁₀₇	C₄⋊C₈
prime radical	C₂³×C₁₀₇	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₀₇ ◁ C₂²×C₈×C₁₀₇ ◁ G

148 conjugacy classes of subgroups.

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)(5,6,8,13,9,12,16,19,10,14,17,20,7,11,15,18)(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)(6,11,14,12)(13,18,20,19)

Conjugacy classes & character table

5992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#7107, C₁₀₇×#7108, C₁₀₇×#7114, …
maximal normal subgroup of	C₁₀₇×#7107, C₁₀₇×#7108, C₁₀₇×#7114, …
maximal quotient of	C₁₀₇×#7138, C₁₀₇×#7143, C₁₀₇×#7146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 108);

C107×#1376 #28332059