Finite Group Databasebeta

← Prev (#14522001) Next (#14522003) →

H(3,𝔽3)×D37 #14522002

order1998
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C32

Aliases

direct productH(3,𝔽3)×D37

Splittings

Fitting, HallH(3,𝔽3)×C37 ⋊ C2
SylowC37 ⋊ C2×H(3,𝔽3)

Subgroups

subgroupG/H
center, FrattiniC3C32×D37
commutator, socle, cosocleC3×C37C2×C32
FittingH(3,𝔽3)×C37C2
hypercenterH(3,𝔽3)D37
hypocenterC37C2×H(3,𝔽3)
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ H(3,𝔽3)

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 333

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,4)(3,6,8)(5,9,7)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(2,5,6)(4,8,9)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1998, 32);