C₂×#367×C₁₁₃ #28386953

order	14464
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×#367×C₁₁₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁₃	D₈
commutator	C₈	C₂²×C₄×C₁₁₃
Frattini, cosocle	C₂×C₈	C₂³×C₁₁₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂²×C₄×C₁₁₃ ◁ C₂²×C₈×C₁₁₃ ◁ G

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 135
transitive degree	μ_t(G) = 14464

A minimal faithful permutation representation — 3 generators on 135 points:

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

Conjugacy classes & character table

4972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁₃×#7474, C₁₁₃×#7477, C₄×#367×C₁₁₃, …
maximal normal subgroup of	C₁₁₃×#7474, C₁₁₃×#7477, C₄×#367×C₁₁₃, …
maximal quotient of	C₂×C₁₁₃×#1372, C₁₁₃×#12023, C₁₁₃×#12033, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 889);

C2×#367×C113 #28386953