Finite Group Databasebeta

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C5×C11×D7×C3⋊D3 #28357694

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C11×D7×C3⋊D3
unambiguous semidirect product(C3×D7)⋊(C5×D3×C11)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derived, HallC32×C7 ⋊ C22×C5×C11
HallC32×C7×C11 ⋊ C22×C5
HallC32×C5×C11 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C22×C11
HallC32×C11 ⋊ C2×C5×D7
HallC7×C11 ⋊ C2×C5×C3⋊D3
HallC32×C5 ⋊ C2×C11×D7
HallC5×C7 ⋊ C2×C11×C3⋊D3
SylowC32 ⋊ C2×C5×C11×D7
SylowC7 ⋊ C2×C5×C11×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC5×C11D7×C3⋊D3
commutator, cosocle, hypocenterC32×C7C22×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C32×C7
UCSC1 ◁ C5×C11

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 3465

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 361);