C₂⁶×D₁₁₃ #28405388

order	14464
isoclinism	isoclinic class of D₁₁₃
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²¹

Aliases

direct product	C₂⁶×D₁₁₃
unambiguous semidirect product	C₁₁₃⋊C₂⁷
unambiguous semidirect product	(C₂×C₁₁₃)⋊C₂⁶

Splittings

Fitting, socle	C₂⁶×C₁₁₃ ⋊ C₂
derived, Sylow	C₁₁₃ ⋊ C₂⁷

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁶	D₁₁₃
commutator, cosocle, hypocenter	C₁₁₃	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₁₁₃	C₂
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂⁶

58424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 7 generators on 125 points:

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

Conjugacy classes & character table

3712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19324);

C26×D113 #28405388