Finite Group Databasebeta

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C3×C11⋊C5×D103 #46800931

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

Aliases

direct productC3×C11⋊C5×D103
unambiguous semidirect product(C3×C11×D103)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D103
commutator, cosocle, hypocenterC11×C103C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C103C2×C5
LCSG ▷ C11×C103
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3399

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 20);