Finite Group Databasebeta

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C3×C7×D33⋊D13 #49114907

order36036
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC3×C7×D33⋊D13
unambiguous semidirect productD33⋊(C3×C7×D13)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derivedC3×C11×C13 ⋊ C22×C3×C7
HallC32×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C2×C3×D3
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3×D3×C7
HallC32×C13 ⋊ C2×C7×D11
HallC32×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C3×D3×D11
HallC7×C11 ⋊ C3×D3×D13
HallC32×C7 ⋊ D11×D13
SylowC13 ⋊ C3×D3×C7×D11
SylowC11 ⋊ C3×D3×C7×D13
SylowC32 ⋊ C7×D11×D13

Subgroups

subgroupG/H
center, hypercenterC3×C7D33⋊D13
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C3×C7

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

2709 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 575);