Finite Group Databasebeta

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C3×D33×D91 #49114922

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

Aliases

direct productC3×D33×D91

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derivedC3×C7×C11×C13 ⋊ C22×C3
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×C3×D3
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C3×D3×D7
HallC32×C13 ⋊ D7×D11
HallC32×C11 ⋊ C2×D91
HallC7×C13 ⋊ C2×C3×D33
HallC7×C11 ⋊ C3×D3×D13
HallC32×C7 ⋊ D11×D13
SylowC13 ⋊ C3×D7×D33
SylowC11 ⋊ C3×D3×D91
SylowC32 ⋊ D11×D91
SylowC7 ⋊ C3×D13×D33

Subgroups

subgroupG/H
center, hypercenterC3D33×D91
commutator, cosocle, hypocenterC3×C7×C11×C13C22×C3
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C3×C7×C11×C13
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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

2538 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 590);