D₁₃×(C₁₁⋊C₅)⋊D₁₁ #44538165

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

Aliases

direct product	D₁₃×(C₁₁⋊C₅)⋊D₁₁
unambiguous semidirect product	(D₁₃×C₁₁⋊C₅)⋊D₁₁

Splittings

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

Subgroups

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

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 715

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 105);

D13×(C11⋊C5)⋊D11 #44538165