Finite Group Databasebeta

← Prev (#45686801) Next (#45686803) →

C3×#26013199 #45686802

order33330
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#26013199

Splittings

Fitting, socle, HallC3×C11×C101 ⋊ C2×C5
derived, HallC11×C101 ⋊ C2×C3×C5
HallC3×#19149920 ⋊ C2
HallC3×D11×C101 ⋊ C5
Hall#19149920 ⋊ C2×C3
HallD11×C101 ⋊ C3×C5
HallC3×C101 ⋊ AGL(1,𝔽11)
SylowC101 ⋊ C3×AGL(1,𝔽11)
HallC3×D11 ⋊ C101⋊C5
HallC3×C11 ⋊ C2×C101⋊C5
HallD11 ⋊ C3×C101⋊C5
SylowC11 ⋊ C2×C3×C101⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#26013199
commutator, cosocle, hypocenterC11×C101C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C11×C101
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

453 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 34);