C₂×#479×C₁₁₃ #28387871

order	14464
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×#479×C₁₁₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂×C₄²×C₁₁₃ ◁ G

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 139
transitive degree	μ_t(G) = 14464

A minimal faithful permutation representation — 4 generators on 139 points:

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

Conjugacy classes & character table

4294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#9246, C₄×#479×C₁₁₃, C₁₁₃×#21618, …
maximal normal subgroup of	C₁₁₃×#9246, C₄×#479×C₁₁₃, C₁₁₃×#21618, …
maximal quotient of	C₂×C₁₁₃×#1805, C₂×C₁₁₃×#1863, C₂×C₁₁₃×#1865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 1807);

C2×#479×C113 #28387871