C₁₀₇×#1406 #28332089

order	13696
nilpotency class	5
isoclinism	isoclinic class of #1406
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₀₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₇×#1406

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₇	#353
commutator	C₄²	C₂×C₄×C₁₀₇
Frattini, cosocle	#124	C₂²×C₁₀₇
prime radical	#496×C₁₀₇	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₇ ◁ C₂²×C₁₀₇ ◁ C₂×C₄×C₁₀₇ ◁ #124×C₁₀₇ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 123 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₀₇×#1406, C₁₀₇×#13577, C₁₀₇×#13578, …
maximal normal subgroup of	C₂×C₁₀₇×#1406, C₁₀₇×#13577, C₁₀₇×#13578, …
maximal quotient of	C₁₀₇×#7352, C₁₀₇×#7372, C₁₀₇×#7402, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 138);

C107×#1406 #28332089