C₁₁₃×#1636 #28386432

order	14464
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁₃×#1636

Subgroups

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

188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 14464

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

(1,2,6,9)(3,10,12,15)(4,8,5,13)(7,14,16,11)(17,18,23,27)(19,28,20,31)(21,26,22,25)(24,30,32,29)(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)(4,11)(5,14)(6,12)(8,15)(9,16)(10,13)(17,19,23,20)(18,24,27,32)(21,30,22,29)(25,31,26,28);(1,4,6,5)(2,8,9,13)(3,11,12,14)(7,15,16,10)(17,20,23,19)(18,24,27,32)(21,29,22,30)(25,31,26,28)

Conjugacy classes & character table

2938 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₁₃×#1636, C₁₁₃×#18494, C₁₁₃×#18519, …
maximal normal subgroup of	C₂×C₁₁₃×#1636, C₁₁₃×#18494, C₁₁₃×#18519, …
maximal quotient of	C₁₁₃×#7763, C₁₁₃×#7769, C₁₁₃×#7771, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 368);