Finite Group Databasebeta

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C3×(C11⋊C5)⋊D103 #46800933

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

Aliases

direct productC3×(C11⋊C5)⋊D103
unambiguous semidirect product(C11⋊C5)⋊(C3×D103)
unambiguous semidirect product(C3×D1133)⋊C5

Splittings

Fitting, socle, HallC3×C11×C103 ⋊ C2×C5
derived, HallC11×C103 ⋊ C2×C3×C5
HallC3×C11⋊C5×C103 ⋊ C2
HallC3×D1133 ⋊ C5
HallC11⋊C5×C103 ⋊ C2×C3
HallD1133 ⋊ C3×C5
HallC3×C103 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D103
SylowC103 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D103
HallC3×C11 ⋊ C5×D103
SylowC11 ⋊ C3×C5×D103

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊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

1104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 22);