Finite Group Databasebeta

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C3×C11×D101⋊C5 #45686791

order33330
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D101⋊C5
unambiguous semidirect productD101⋊(C3×C5×C11)
unambiguous semidirect product(C101⋊C5)⋊(C2×C3×C11)
unambiguous semidirect product(C3×D101)⋊(C5×C11)

Splittings

Fitting, socle, HallC3×C11×C101 ⋊ C2×C5
derived, SylowC101 ⋊ C2×C3×C5×C11
HallC3×C11×C101⋊C5 ⋊ C2
HallC3×C11×D101 ⋊ C5
HallC11×C101⋊C5 ⋊ C2×C3
HallC11×D101 ⋊ C3×C5
HallC3×C101⋊C5 ⋊ C2×C11
HallC11×C101 ⋊ C2×C3×C5
HallC3×D101 ⋊ C5×C11
HallC101⋊C5 ⋊ C2×C3×C11
HallC3×C101 ⋊ C2×C5×C11
HallD101 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11D101⋊C5
commutator, cosocle, hypocenterC101C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C101
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 23);