C₂³×C₄²×C₁₀₇ #28334101

order	13696
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian

C₂³×C₄²×C₁₀₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁵×C₁₀₇
socle, prime radical	C₂⁵×C₁₀₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

3000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 13696

A minimal faithful permutation representation — 5 generators on 121 points:

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

Conjugacy classes & character table

13696 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₇×#7554, C₁₀₇×#10712, C₁₀₇×#10719, …
maximal normal subgroup of	C₁₀₇×#7554, C₁₀₇×#10712, C₁₀₇×#10719, …
maximal quotient of	C₂²×C₄³×C₁₀₇, C₂³×#95×C₁₀₇, C₂²×#376×C₁₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 2150);

C23×C42×C107 #28334101