C₂×#432×C₁₀₇ #28333601

order	13696
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#432×C₁₀₇

Subgroups

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

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 6848

A minimal faithful permutation representation — 4 generators on 125 points:

(1,2)(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);(3,4)(5,8)(6,7)(9,10)(11,12,13,16,14,15,17,18);(4,7)(8,10);(3,5,6,9)(4,8,7,10)(12,15)(16,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₇×#7863, C₁₀₇×#7864, C₁₀₇×#7875, …
maximal normal subgroup of	C₁₀₇×#7863, C₁₀₇×#7864, C₁₀₇×#7875, …
maximal quotient of	C₂×C₁₀₇×#1745, C₂×C₁₀₇×#1749, C₂×C₁₀₇×#1767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 1650);

C2×#432×C107 #28333601