Finite Group Databasebeta

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C3×(C11⋊C5)⋊D101 #45686804

order33330
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C11⋊C5)⋊D101
unambiguous semidirect product(C11⋊C5)⋊(C3×D101)

Splittings

Fitting, socle, HallC3×C11×C101 ⋊ C2×C5
derived, HallC11×C101 ⋊ C2×C3×C5
HallC3×C11⋊C5×C101 ⋊ C2
HallC3×D1111 ⋊ C5
HallC11⋊C5×C101 ⋊ C2×C3
HallD1111 ⋊ C3×C5
HallC3×C101 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D101
SylowC101 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D101
HallC3×C11 ⋊ C5×D101
SylowC11 ⋊ C3×C5×D101

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊D101
commutator, cosocle, hypocenterC11×C101C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C11×C101
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

1083 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 36);