Finite Group Databasebeta

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C2×C3×C11×D255 #46778206

order33660
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D255
unambiguous semidirect product(C2×C3)⋊(C3×C11×D85)
unambiguous semidirect product(C2×C5)⋊(C3×C11×D51)
unambiguous semidirect product(C2×C17)⋊(C3×C11×D15)

Splittings

Fitting, socleC2×C32×C5×C11×C17 ⋊ C2
derivedC3×C5×C17 ⋊ C22×C3×C11
HallC32×C5×C11×C17 ⋊ C22
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3×D3
HallC32×C5×C17 ⋊ C22×C11
HallC32×C5×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C3×D15
HallC32×C17 ⋊ C2×D5×C11
HallC32×C11 ⋊ C2×D85
HallC5×C17 ⋊ C2×C3×D3×C11
HallC5×C11 ⋊ C2×C3×D51
HallC32×C5 ⋊ C2×C11×D17
SylowC17 ⋊ C2×C3×C11×D15
SylowC32 ⋊ C2×C11×D85
SylowC5 ⋊ C2×C3×C11×D51

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D255
commutator, cosocle, hypocenterC3×C5×C17C22×C3×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C3×C11

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 11220

Conjugacy classes & character table

8514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 374);