D₁₁₉₅₁ #37560757

order	23902
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₉₅₁
unambiguous semidirect product	C₁₇⋊D₇₀₃
unambiguous semidirect product	C₁₉⋊D₆₂₉
unambiguous semidirect product	C₃₇⋊D₃₂₃

Splittings

Fitting, socle, derived, Hall	C₁₇×C₁₉×C₃₇ ⋊ C₂
Hall	C₁₉×C₃₇ ⋊ D₁₇
Hall	C₁₇×C₃₇ ⋊ D₁₉
Hall	C₁₇×C₁₉ ⋊ D₃₇
Sylow	C₃₇ ⋊ D₃₂₃
Sylow	C₁₉ ⋊ D₆₂₉
Sylow	C₁₇ ⋊ D₇₀₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₁₉×C₃₇	C₂
LCS	G ▷ C₁₇×C₁₉×C₃₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 11951

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

2,17,19,37|b^a=b^16,c^a=c^18,d^a=d^36

Conjugacy classes & character table

5977 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23902, 8);

D11951 #37560757