D₁₁₆₈₇ #37552626

order	23374
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₆₈₇
unambiguous semidirect product	C₁₃⋊D₈₉₉
unambiguous semidirect product	C₂₉⋊D₄₀₃
unambiguous semidirect product	C₃₁⋊D₃₇₇

Splittings

Fitting, socle, derived, Hall	C₁₃×C₂₉×C₃₁ ⋊ C₂
Hall	C₂₉×C₃₁ ⋊ D₁₃
Hall	C₁₃×C₃₁ ⋊ D₂₉
Hall	C₁₃×C₂₉ ⋊ D₃₁
Sylow	C₃₁ ⋊ D₃₇₇
Sylow	C₂₉ ⋊ D₄₀₃
Sylow	C₁₃ ⋊ D₈₉₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₂₉×C₃₁	C₂
LCS	G ▷ C₁₃×C₂₉×C₃₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 11687

A minimal faithful permutation representation — 2 generators on 73 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Polycyclic presentation:

2,13,29,31|b^a=b^12,c^a=c^28,d^a=d^30

Conjugacy classes & character table

5845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23374, 8);

D11687 #37552626