D₁₅₂₈₃ #44479887

order	30566
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₂₈₃
unambiguous semidirect product	C₁₇⋊D₈₉₉
unambiguous semidirect product	C₂₉⋊D₅₂₇
unambiguous semidirect product	C₃₁⋊D₄₉₃

Splittings

Fitting, socle, derived, Hall	C₁₇×C₂₉×C₃₁ ⋊ C₂
Hall	C₂₉×C₃₁ ⋊ D₁₇
Hall	C₁₇×C₃₁ ⋊ D₂₉
Hall	C₁₇×C₂₉ ⋊ D₃₁
Sylow	C₃₁ ⋊ D₄₉₃
Sylow	C₂₉ ⋊ D₅₂₇
Sylow	C₁₇ ⋊ D₈₉₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₂₉×C₃₁	C₂
LCS	G ▷ C₁₇×C₂₉×C₃₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 15283

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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)

Polycyclic presentation:

2,17,29,31|b^a=b^16,c^a=c^28,d^a=d^30

Conjugacy classes & character table

7643 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₂₈₃
maximal normal subgroup of	C₂×D₁₅₂₈₃
maximal quotient of	Dic₁₅₂₈₃, C₂×D₁₅₂₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30566, 8);

D15283 #44479887