Finite Group Databasebeta

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C32×D7×D55 #28357657

order13860
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D7×D55

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C22
derived, HallC5×C7×C11 ⋊ C22×C32
HallC32×C7×C11 ⋊ C2×D5
HallC32×C5×C11 ⋊ C2×D7
HallC32×C5×C7 ⋊ C2×D11
HallC32×C11 ⋊ D5×D7
HallC7×C11 ⋊ C2×C32×D5
HallC32×C7 ⋊ C2×D55
HallC5×C11 ⋊ C2×C32×D7
HallC32×C5 ⋊ D7×D11
HallC5×C7 ⋊ C2×C32×D11
SylowC11 ⋊ C32×D5×D7
SylowC7 ⋊ C2×C32×D55
SylowC5 ⋊ C32×D7×D11

Subgroups

subgroupG/H
center, hypercenterC32D7×D55
commutator, cosocle, hypocenterC5×C7×C11C22×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C11C22
LCSG ▷ C5×C7×C11
UCSC1 ◁ C32

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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

1305 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 324);