C₁₀₇×#3285 #28333968

order	13696
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₇×#3285

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₄×D₄×C₁₀₇ ◁ G

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 127
transitive degree	μ_t(G) = 6848

A minimal faithful permutation representation — 4 generators on 127 points:

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

Conjugacy classes & character table

3745 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#33831, C₁₀₇×#33835, C₁₀₇×#33836, …
maximal normal subgroup of	C₁₀₇×#33831, C₁₀₇×#33835, C₁₀₇×#33836, …
maximal quotient of	C₁₀₇×#19835, C₁₀₇×#19836, C₁₀₇×#19837, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 2017);

C107×#3285 #28333968