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Dic493 #14520303

order1972
isoclinismisoclinic class of D493
automorphismAut(G) order 441728
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic493

Splittings

derived, HallC17×C29 ⋊ C4
SylowC29 ⋊ Dic17
SylowC17 ⋊ Dic29

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D493
commutator, hypocenterC17×C29C4
Fitting, socle, prime radical, cosocleC2×C17×C29C2
LCSG ▷ C17×C29
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 1972

A minimal faithful permutation representation — 2 generators on 50 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);(1,3,2,4)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Polycyclic presentation:

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

Conjugacy classes & character table

496 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×Dic493, Dic3451, Dic493⋊C7, …
maximal normal subgroup ofC7×Dic493, Dic493⋊C7, C11×Dic493, …
maximal quotient ofC7×Dic493, Dic3451, #31801698, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1972, 3);