D₁₃₀₇₉ #39908555

order	26158
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₀₇₉
unambiguous semidirect product	C₁₁⋊D₁₁₈₉
unambiguous semidirect product	C₂₉⋊D₄₅₁
unambiguous semidirect product	C₄₁⋊D₃₁₉

Splittings

Fitting, socle, derived, Hall	C₁₁×C₂₉×C₄₁ ⋊ C₂
Hall	C₂₉×C₄₁ ⋊ D₁₁
Hall	C₁₁×C₄₁ ⋊ D₂₉
Hall	C₁₁×C₂₉ ⋊ D₄₁
Sylow	C₄₁ ⋊ D₃₁₉
Sylow	C₂₉ ⋊ D₄₅₁
Sylow	C₁₁ ⋊ D₁₁₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₂₉×C₄₁	C₂
LCS	G ▷ C₁₁×C₂₉×C₄₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 13079

A minimal faithful permutation representation — 2 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Polycyclic presentation:

2,11,29,41|b^a=b^10,c^a=c^28,d^a=d^40

Conjugacy classes & character table

6541 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₀₇₉
maximal normal subgroup of	C₂×D₁₃₀₇₉
maximal quotient of	Dic₁₃₀₇₉, C₂×D₁₃₀₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26158, 8);

D13079 #39908555