C₁₁₃×#1660 #28386456

order	14464
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁₃×#1660

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₁₃
prime radical	C₂×D₄×C₁₁₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₄²×C₁₁₃ ◁ G

196 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 137
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 3 generators on 137 points:

(2,5)(3,7)(6,8)(9,10,15,19)(11,20,22,23)(12,21,16,24)(13,18,14,17)(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);(3,7)(5,8)(9,11)(10,16)(12,19)(13,24)(14,21)(15,22)(17,23)(18,20);(1,2)(3,8)(4,6)(5,7)(9,12,15,16)(10,11,19,22)(13,23,14,20)(17,21,18,24)

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#13680, C₂×C₁₁₃×#1660, C₁₁₃×#18984, …
maximal normal subgroup of	C₁₁₃×#13680, C₂×C₁₁₃×#1660, C₁₁₃×#18984, …
maximal quotient of	C₁₁₃×#7751, C₁₁₃×#7754, C₁₁₃×#7757, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 392);