Finite Group Databasebeta

← Prev (#45686812) Next (#45686814) →

D3×#19149919 #45686813

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

Aliases

direct productD3×#19149919
unambiguous semidirect productC3⋊(C2×#19149919)

Splittings

Fitting, socle, derived, HallC3×C11×C101 ⋊ C2×C5
HallC3×#19149919 ⋊ C2
HallD3×C11×C101 ⋊ C5
HallC11×C101 ⋊ C5×D3
HallD3×C101 ⋊ C11⋊C5
HallC3×C101 ⋊ C2×C11⋊C5
SylowC101 ⋊ D3×C11⋊C5
HallD3×C11 ⋊ C101⋊C5
HallC3×C11 ⋊ C2×C101⋊C5
SylowC11 ⋊ D3×C101⋊C5
SylowC3 ⋊ C2×#19149919

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C101C2×C5
LCSG ▷ C3×C11×C101
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 45);