Finite Group Databasebeta

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C5×C7×C3⋊D3×D11 #28357692

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C7×C3⋊D3×D11

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derived, HallC32×C11 ⋊ C22×C5×C7
HallC32×C7×C11 ⋊ C22×C5
HallC32×C5×C11 ⋊ C22×C7
HallC5×C7×C11 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D11
HallC7×C11 ⋊ C2×C5×C3⋊D3
HallC32×C7 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C7×C3⋊D3
HallC32×C5 ⋊ C2×C7×D11
SylowC11 ⋊ C2×C5×C7×C3⋊D3
SylowC32 ⋊ C2×C5×C7×D11

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D3×D11
commutator, cosocle, hypocenterC32×C11C22×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C32×C11
UCSC1 ◁ C5×C7

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

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 359);