C₁₀₇×#1829 #28332512

order	13696
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₇×#1829

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₇	#381
commutator	C₂³	C₂²×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₇
prime radical	C₂²×D₄×C₁₀₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ G

272 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:

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

Conjugacy classes & character table

3103 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#12725, C₁₀₇×#12726, C₂×C₁₀₇×#1829, …
maximal normal subgroup of	C₁₀₇×#12725, C₁₀₇×#12726, C₂×C₁₀₇×#1829, …
maximal quotient of	C₁₀₇×#8734, C₁₀₇×#8736, C₁₀₇×#8751, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 561);

C107×#1829 #28332512