Finite Group Databasebeta

← Prev (#46800933) Next (#46800935) →

D3×C11⋊C5×C103 #46800934

order33990
automorphism?
homologyAbelianization (H1) = C2×C5×C103 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11⋊C5×C103
unambiguous semidirect productC3⋊(C2×C11⋊C5×C103)
unambiguous semidirect product(D3×C11)⋊(C5×C103)
unambiguous semidirect product(D3×C11×C103)⋊C5

Splittings

Fitting, socle, HallC3×C11×C103 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C103
HallC3×C11⋊C5×C103 ⋊ C2
HallD3×C11×C103 ⋊ C5
HallC11×C103 ⋊ C5×D3
HallC3×C103 ⋊ C2×C11⋊C5
HallC3×C11⋊C5 ⋊ C2×C103
HallD3×C11 ⋊ C5×C103
SylowC11 ⋊ C5×D3×C103
SylowC3 ⋊ C2×C11⋊C5×C103

Subgroups

subgroupG/H
center, hypercenterC103D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C103
FrattiniC1G
Fitting, socleC3×C11×C103C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C103

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3399

Conjugacy classes & character table

2163 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 23);