Finite Group Databasebeta

← Prev (#46800917) Next (#46800919) →

C3×C5×D1133 #46800918

order33990
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1133

Splittings

Fitting, socle, HallC3×C5×C11×C103 ⋊ C2
derived, HallC11×C103 ⋊ C2×C3×C5
HallC5×C11×C103 ⋊ C2×C3
HallC3×C11×C103 ⋊ C2×C5
HallC3×C5×C103 ⋊ D11
HallC5×C103 ⋊ C3×D11
HallC3×C103 ⋊ C5×D11
HallC3×C5×C11 ⋊ D103
SylowC103 ⋊ C3×C5×D11
HallC5×C11 ⋊ C3×D103
HallC3×C11 ⋊ C5×D103
SylowC11 ⋊ C3×C5×D103

Subgroups

subgroupG/H
center, hypercenterC3×C5D1133
commutator, cosocle, hypocenterC11×C103C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C103C2
LCSG ▷ C11×C103
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16995

Conjugacy classes & character table

8520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 7);