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C7×(C3⋊D3)⋊D55 #28357752

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

Aliases

direct productC7×(C3⋊D3)⋊D55
unambiguous semidirect product(C3⋊D3)⋊(C7×D55)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derived, HallC32×C5×C11 ⋊ C22×C7
HallC32×C7×C11 ⋊ C2×D5
HallC5×C7×C11 ⋊ D32
HallC32×C5×C7 ⋊ C2×D11
HallC32×C11 ⋊ C2×C7×D5
HallC7×C11 ⋊ (C3⋊D3)⋊D5
HallC32×C7 ⋊ C2×D55
HallC5×C11 ⋊ D32×C7
HallC32×C5 ⋊ C2×C7×D11
HallC5×C7 ⋊ (C3⋊D3)⋊D11
SylowC11 ⋊ C7×(C3⋊D3)⋊D5
SylowC32 ⋊ C2×C7×D55
SylowC5 ⋊ C7×(C3⋊D3)⋊D11

Subgroups

subgroupG/H
center, hypercenterC7(C3⋊D3)⋊D55
commutator, cosocle, hypocenterC32×C5×C11C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C32×C5×C11
UCSC1 ◁ C7

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 2310

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 419);