C₁₁₃×#1662 #28386458

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

Aliases

direct product

C₁₁₃×#1662

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₁₃
prime radical	#562×C₁₁₃	C₂
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) = 145
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 3 generators on 145 points:

(1,2,6,10)(3,11,13,16)(4,9,5,8)(7,14,15,12)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(1,3)(2,7)(4,14)(5,12)(6,13)(8,16)(9,11)(10,15)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(1,3)(2,7)(4,12)(5,14)(6,13)(8,11)(9,16)(10,15)(20,30)(23,28)(25,32)(26,29)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₁₃×#7525, C₂×C₁₁₃×#1662, C₁₁₃×#18987, …
maximal normal subgroup of	C₁₁₃×#7525, C₂×C₁₁₃×#1662, C₁₁₃×#18987, …
maximal quotient of	C₁₁₃×#7762, C₁₁₃×#7769, C₁₁₃×#7773, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 394);