D₁₁₀₆₃ #36348956

order	22126
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₀₆₃
unambiguous semidirect product	C₁₃⋊D₈₅₁
unambiguous semidirect product	C₂₃⋊D₄₈₁
unambiguous semidirect product	C₃₇⋊D₂₉₉

Splittings

Fitting, socle, derived, Hall	C₁₃×C₂₃×C₃₇ ⋊ C₂
Hall	C₂₃×C₃₇ ⋊ D₁₃
Hall	C₁₃×C₃₇ ⋊ D₂₃
Hall	C₁₃×C₂₃ ⋊ D₃₇
Sylow	C₃₇ ⋊ D₂₉₉
Sylow	C₂₃ ⋊ D₄₈₁
Sylow	C₁₃ ⋊ D₈₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₂₃×C₃₇	C₂
LCS	G ▷ C₁₃×C₂₃×C₃₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 11063

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)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Polycyclic presentation:

2,13,23,37|b^a=b^12,c^a=c^22,d^a=d^36

Conjugacy classes & character table

5533 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22126, 8);

D11063 #36348956