Finite Group Databasebeta

← Prev (#67314) Next (#67316) →

Cayley diagram

D3×D31 #67315

order372
isoclinismisoclinic class of D3×D31
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D31
unambiguous semidirect product(D3×C31)⋊C2
unambiguous semidirect product(C3×D31)⋊C2
unambiguous semidirect productD93⋊C2

Splittings

Fitting, socle, derived, HallC3×C31 ⋊ C22
SylowC31 ⋊ C2×D3
SylowC3 ⋊ C2×D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C31C22
LCSG ▷ C3×C31
UCSC1

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

Conjugacy classes & character table

51 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×D31, D9×D31, D3×D31⋊C3, …
maximal normal subgroup ofC2×D3×D31, D3×D31⋊C3, C3×D3×D31, …
maximal quotient ofDic3×D31, D3×Dic31, D93⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(372, 8);