D₉₈₂₃ #34087333

order	19646
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₈₂₃
unambiguous semidirect product	C₁₁⋊D₈₉₃
unambiguous semidirect product	C₁₉⋊D₅₁₇
unambiguous semidirect product	C₄₇⋊D₂₀₉

Splittings

Fitting, socle, derived, Hall	C₁₁×C₁₉×C₄₇ ⋊ C₂
Hall	C₁₉×C₄₇ ⋊ D₁₁
Hall	C₁₁×C₄₇ ⋊ D₁₉
Hall	C₁₁×C₁₉ ⋊ D₄₇
Sylow	C₄₇ ⋊ D₂₀₉
Sylow	C₁₉ ⋊ D₅₁₇
Sylow	C₁₁ ⋊ D₈₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₉×C₄₇	C₂
LCS	G ▷ C₁₁×C₁₉×C₄₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 9823

A minimal faithful permutation representation — 2 generators on 77 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)

Polycyclic presentation:

2,11,19,47|b^a=b^10,c^a=c^18,d^a=d^46

Conjugacy classes & character table

4913 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19646, 8);

D9823 #34087333