#127×C₁₀₇ #16811997

order	3424
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

#127×C₁₀₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₁₀₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 115
transitive degree	μ_t(G) = 1712

A minimal faithful permutation representation — 3 generators on 115 points:

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

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#331×C₁₀₇, #353×C₁₀₇, #453×C₁₀₇, …
maximal normal subgroup of	#331×C₁₀₇, #353×C₁₀₇, #453×C₁₀₇, …
maximal quotient of	#384×C₁₀₇, #390×C₁₀₇, #392×C₁₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3424, 34);

#127×C107 #16811997