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Cayley diagram

D73⋊C3 #89141

order438
isoclinismisoclinic class of D73⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productD73⋊C3
unambiguous semidirect product(C73⋊C3)⋊C2

Splittings

Fitting, socle, derived, SylowC73 ⋊ C2×C3
HallC73⋊C3 ⋊ C2
HallD73 ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC73C2×C3
LCSG ▷ C73
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 73

A minimal faithful permutation representation — 2 generators on 73 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,60)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,48,57,34,49,63)(37,42,62,50,51,58)(40,67,65,54,55,53)(52,61,68,56,64,72)(59,73,71,69,70,66);(1,2,5,11,19,32,33,20,4,8,13,23,37,52,54,36,10,16,24,38,53,66,69,51,18,29,39,41,57,68,73,64,31,48,55,58,60,47,62,67,49,46,61,70,72,63,28,43,44,27,42,59,71,65,45,15,26,14,25,40,56,50,35,22,7,6,12,21,34,30,17,9,3)

Polycyclic presentation:

2,3,73|c^a=c^72,c^b=c^8

Conjugacy classes & character table

18 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#64408⋊C3, C2×D73⋊C3, #10620323⋊C2, …
maximal normal subgroup of#64408⋊C3, C2×D73⋊C3, #10620323⋊C2, …
maximal quotient ofDic73⋊C3, C2×D73⋊C3, #10620321⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(438, 1);