C₁₀₇×#2091 #28332774

order	13696
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₇×#2091

Subgroups

	subgroup	G/H
center	C₄×C₁₀₇	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₇
socle	C₂×C₁₀₇	#399
prime radical	C₂⁴×C₁₀₇	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ G

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 1712

A minimal faithful permutation representation — 3 generators on 123 points:

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

Conjugacy classes & character table

2782 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#7432, C₁₀₇×#7433, C₁₀₇×#12298, …
maximal normal subgroup of	C₁₀₇×#7432, C₁₀₇×#7433, C₁₀₇×#12298, …
maximal quotient of	C₁₀₇×#10659, C₁₀₇×#10660, C₁₀₇×#10661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 823);

C107×#2091 #28332774