Finite Group Databasebeta

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C5×C11×#64422⋊C2 #44568639

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×#64422⋊C2
unambiguous semidirect product#64422⋊(C2×C5×C11)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C22×C3
derived, SylowC72 ⋊ C22×C3×C5×C11
HallC5×C11×D72 ⋊ C3
HallC5×C11×#3862 ⋊ C22
HallC11×D72 ⋊ C3×C5
HallC11×#3862 ⋊ C22×C5
HallC5×D72 ⋊ C3×C11
HallC5×#3862 ⋊ C22×C11
HallC72×C11 ⋊ C22×C3×C5
HallC5×C72 ⋊ C22×C3×C11
HallD72 ⋊ C3×C5×C11
Hall#3862 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11#64422⋊C2
commutator, cosocle, hypocenterC72C22×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C22×C3
LCSG ▷ C72
UCSC1 ◁ C5×C11

168 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 60 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

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 341);