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Dic483 #14515376

order1932
isoclinismisoclinic class of D483
automorphismAut(G) order 255024
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic483
unambiguous semidirect productC3⋊Dic161
unambiguous semidirect productC7⋊Dic69
unambiguous semidirect productC23⋊Dic21

Splittings

derived, HallC3×C7×C23 ⋊ C4
HallC7×C23 ⋊ Dic3
HallC3×C23 ⋊ Dic7
SylowC23 ⋊ Dic21
HallC3×C7 ⋊ Dic23
SylowC7 ⋊ Dic69
SylowC3 ⋊ Dic161

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D483
commutator, hypocenterC3×C7×C23C4
Fitting, socle, prime radical, cosocleC2×C3×C7×C23C2
LCSG ▷ C3×C7×C23
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1932

A minimal faithful permutation representation — 2 generators on 37 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);(1,3,2,4)(6,7)(9,14)(10,13)(11,12)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Polycyclic presentation:

2^2,3,7,23|a^2=b,c^a=c^2,d^a=d^6,e^a=e^22

Conjugacy classes & character table

486 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3381, C7×Dic483, C3⋊(C7⋊Dic161), …
maximal normal subgroup ofC7×Dic483, C11×Dic483, C3⋊(C7⋊(Dic23⋊C11)), …
maximal quotient ofDic3381, C7×Dic483, C3⋊(C7⋊Dic161), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1932, 11);