Finite Group Databasebeta

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D3×C11×C101⋊C5 #45686809

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

Aliases

direct productD3×C11×C101⋊C5
unambiguous semidirect productC3⋊(C2×C11×C101⋊C5)
unambiguous semidirect product(D3×C101)⋊(C5×C11)

Splittings

Fitting, socle, HallC3×C11×C101 ⋊ C2×C5
derived, HallC3×C101 ⋊ C2×C5×C11
HallC3×C11×C101⋊C5 ⋊ C2
HallD3×C11×C101 ⋊ C5
HallC3×C101⋊C5 ⋊ C2×C11
HallC11×C101 ⋊ C5×D3
HallD3×C101 ⋊ C5×C11
SylowC101 ⋊ C5×D3×C11
HallC3×C11 ⋊ C2×C101⋊C5
SylowC3 ⋊ C2×C11×C101⋊C5

Subgroups

subgroupG/H
center, hypercenterC11D3×C101⋊C5
commutator, cosocle, hypocenterC3×C101C2×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C101C2×C5
LCSG ▷ C3×C101
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3333

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 41);