Finite Group Databasebeta

← Prev (#90900) Next (#90902) →

Cayley diagram

D79⋊C3 #90901

order474
isoclinismisoclinic class of D79⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productD79⋊C3
unambiguous semidirect product(C79⋊C3)⋊C2

Splittings

Fitting, socle, derived, SylowC79 ⋊ C2×C3
HallC79⋊C3 ⋊ C2
HallD79 ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC79C2×C3
LCSG ▷ C79
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 79

A minimal faithful permutation representation — 2 generators on 79 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)(19,46,47,30,31,63)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,67,68,49,50,78)(34,66,51,52,48,60)(37,42,65,54,55,61)(40,74,73,58,59,57)(53,79,71,70,69,76)(56,64,75,72,62,77);(1,2,5,11,19,32,51,28,43,44,27,42,62,31,48,59,61,63,76,70,52,33,20,4,8,13,23,37,56,73,45,15,26,14,25,40,50,69,68,75,77,78,79,67,58,36,10,16,24,38,57,72,54,35,22,7,6,12,21,34,53,71,47,65,74,66,46,64,55,18,29,39,41,60,49,30,17,9,3)

Polycyclic presentation:

2,3,79|c^a=c^78,c^b=c^23

Conjugacy classes & character table

19 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D79⋊C3, C3×D79⋊C3, C3⋊(D79⋊C3), …
maximal normal subgroup ofC2×D79⋊C3, C3×D79⋊C3, C5×D79⋊C3, …
maximal quotient of(C79⋊C3)⋊C4, C2×D79⋊C3, D79⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(474, 1);