D₉₅₀₃ #34039615

order	19006
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₅₀₃
unambiguous semidirect product	C₁₃⋊D₇₃₁
unambiguous semidirect product	C₁₇⋊D₅₅₉
unambiguous semidirect product	C₄₃⋊D₂₂₁

Splittings

Fitting, socle, derived, Hall	C₁₃×C₁₇×C₄₃ ⋊ C₂
Hall	C₁₇×C₄₃ ⋊ D₁₃
Hall	C₁₃×C₄₃ ⋊ D₁₇
Hall	C₁₃×C₁₇ ⋊ D₄₃
Sylow	C₄₃ ⋊ D₂₂₁
Sylow	C₁₇ ⋊ D₅₅₉
Sylow	C₁₃ ⋊ D₇₃₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₄₃	C₂
LCS	G ▷ C₁₃×C₁₇×C₄₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 9503

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)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,73)(33,72)(34,71)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Polycyclic presentation:

2,13,17,43|b^a=b^12,c^a=c^16,d^a=d^42

Conjugacy classes & character table

4753 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄₃×D₂₂₁, D₁₇×D₅₅₉, D₁₃×D₇₃₁, …
maximal normal subgroup of	D₄₃×D₂₂₁, D₁₇×D₅₅₉, D₁₃×D₇₃₁, …
maximal quotient of	Dic₉₅₀₃, C₂×D₉₅₀₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19006, 8);

D9503 #34039615