C₁₁₃×#3390 #28388186

order	14464
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁₃×#3390

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₄×Q₈×C₁₁₃ ◁ G

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 137
transitive degree	μ_t(G) = 14464

A minimal faithful permutation representation — 4 generators on 137 points:

(1,2,5,4)(3,7,8,6)(9,10)(11,18)(12,16)(13,21)(14,17)(15,20)(19,24)(22,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,3,5,8)(2,6,4,7)(11,19)(15,23)(18,24)(20,22);(9,11,14,19)(10,15,17,23)(12,20,13,22)(16,24,21,18);(1,4,5,2)(3,6,8,7)(9,12,14,13)(10,16,17,21)(11,20,19,22)(15,24,23,18)

Conjugacy classes & character table

3277 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#12361, C₁₁₃×#12363, C₁₁₃×#12413, …
maximal normal subgroup of	C₁₁₃×#12361, C₁₁₃×#12363, C₁₁₃×#12413, …
maximal quotient of	C₁₁₃×#22527, C₁₁₃×#22675, C₁₁₃×#22679, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 2122);

C113×#3390 #28388186