C₅×D₁₃×C₁₁⋊D₁₁ #44538239

order	31460
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂×C₁₁

Aliases

direct product

C₅×D₁₃×C₁₁⋊D₁₁

Splittings

Fitting, socle, Hall	C₅×C₁₁²×C₁₃ ⋊ C₂²
derived, Hall	C₁₁²×C₁₃ ⋊ C₂²×C₅
Hall	C₅×C₁₁² ⋊ C₂×D₁₃
Sylow	C₁₁² ⋊ C₂×C₅×D₁₃
Hall	C₅×C₁₃ ⋊ C₂×C₁₁⋊D₁₁
Sylow	C₁₃ ⋊ C₂×C₅×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₁₃×C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₁₁²×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²×C₁₃	C₂²
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁ ◁ C₅

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 7865

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29,31,33,35,37,39,40,38,36,34,32,30);(17,18,20,22,24,26,27,25,23,21,19)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40);(6,7,9,11,13,15,16,14,12,10,8)

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 179);

C5×D13×C11⋊D11 #44538239