D₉₉₄₅ #34091032

order	19890
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₉₄₅
unambiguous semidirect product	C₅⋊D₁₉₈₉
unambiguous semidirect product	C₉⋊D₁₁₀₅
unambiguous semidirect product	C₁₃⋊D₇₆₅
unambiguous semidirect product	C₁₇⋊D₅₈₅

Splittings

Fitting, derived, Hall	C₅×C₉×C₁₃×C₁₇ ⋊ C₂
Hall	C₉×C₁₃×C₁₇ ⋊ D₅
Hall	C₅×C₁₃×C₁₇ ⋊ D₉
Hall	C₅×C₉×C₁₇ ⋊ D₁₃
Hall	C₅×C₉×C₁₃ ⋊ D₁₇
Hall	C₁₃×C₁₇ ⋊ D₄₅
Hall	C₉×C₁₇ ⋊ D₆₅
Hall	C₉×C₁₃ ⋊ D₈₅
Hall	C₅×C₁₇ ⋊ D₁₁₇
Hall	C₅×C₁₃ ⋊ D₁₅₃
Hall	C₅×C₉ ⋊ D₂₂₁
Sylow	C₁₇ ⋊ D₅₈₅
Sylow	C₁₃ ⋊ D₇₆₅
Sylow	C₉ ⋊ D₁₁₀₅
Sylow	C₅ ⋊ D₁₉₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₃×C₁₇	C₂
Frattini	C₃	D₃₃₁₅
socle	C₃×C₅×C₁₃×C₁₇	D₃
LCS	G ▷ C₅×C₉×C₁₃×C₁₇
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 9945

A minimal faithful permutation representation — 2 generators on 44 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);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Polycyclic presentation:

2,3,5,13,17,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^12,e^a=e^16,f^a=f^2

Conjugacy classes & character table

4974 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉₈₃₅
maximal quotient of	D₂₉₈₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 17);

D9945 #34091032