C₁₁₃×#1366 #28386162

order	14464
nilpotency class	4
isoclinism	isoclinic class of #1366
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁₃×#1366

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁₃	#333
commutator	C₄²	C₂×C₄×C₁₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₁₃
prime radical	C₂²×C₁₁₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁₃ ◁ C₂×C₄×C₁₁₃ ◁ C₄×C₈×C₁₁₃ ◁ G

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 145
transitive degree	μ_t(G) = 3616

A minimal faithful permutation representation — 2 generators on 145 points:

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

Conjugacy classes & character table

2599 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₁₃×#1366, C₁₁₃×#11956, C₁₁₃×#11989, …
maximal normal subgroup of	C₂×C₁₁₃×#1366, C₁₁₃×#11956, C₁₁₃×#11989, …
maximal quotient of	C₁₁₃×#7135, C₁₁₃×#7271, C₂×C₁₁₃×#1366

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 98);

C113×#1366 #28386162