Finite Group Databasebeta

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C32×C5×D11×D17 #46778060

order33660
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×C5×D11×D17

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C22
derived, HallC11×C17 ⋊ C22×C32×C5
HallC32×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C22×C32
HallC32×C5×C17 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D17
HallC32×C17 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D17
HallC5×C17 ⋊ C2×C32×D11
HallC5×C11 ⋊ C2×C32×D17
SylowC17 ⋊ C2×C32×C5×D11
SylowC11 ⋊ C2×C32×C5×D17

Subgroups

subgroupG/H
center, hypercenterC32×C5D11×D17
commutator, cosocle, hypocenterC11×C17C22×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C17C22
LCSG ▷ C11×C17
UCSC1 ◁ C32×C5

240 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 8415

Conjugacy classes & character table

3150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 228);