Finite Group Databasebeta

← Prev (#63293) Next (#63295) →

Cayley diagram

C3×C31⋊C3 #63294

order279
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C31⋊C3
unambiguous semidirect productC31⋊C32
unambiguous semidirect product(C3×C31)⋊C3

Splittings

Fitting, socleC3×C31 ⋊ C3
derived, SylowC31 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3C31⋊C3
commutator, cosocle, hypocenterC31C32
FrattiniC1G
Fitting, socleC3×C31C3
LCSG ▷ C31
UCSC1 ◁ C3

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 93

A minimal faithful permutation representation — 2 generators on 34 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,21)(11,17,19)(13,15,16)(18,24,28)(20,25,26)(22,29,23)(27,30,31);(1,2,4,8,15,5,9,16,23,29,12,19,26,14,22,21,28,31,24,7,13,20,27,30,17,3,6,11,18,25,10)(32,33,34)

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D31⋊C3, D3×C31⋊C3, C3⋊(D31⋊C3), …
maximal normal subgroup ofC3×D31⋊C3, D3×C31⋊C3, C3⋊(D31⋊C3), …
maximal quotient ofC2×C3×C31⋊C3, C9×C31⋊C3, #11719686, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(279, 3);