Finite Group Databasebeta

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C2×C11×C5⋊#64425 #44568799

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C11×C5⋊#64425
unambiguous semidirect product(C2×C5)⋊(C11×#64425)

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2×C3
derived, HallC5×C72 ⋊ C22×C3×C11
HallC2×C11×C5⋊(C7⋊D7) ⋊ C3
HallC5×C11×#3862 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC11×#3862 ⋊ C2×D5
HallC2×C5⋊(C7⋊D7) ⋊ C3×C11
HallC5×#3862 ⋊ C22×C11
HallC72×C11 ⋊ C2×C3×D5
Hall#3862 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×#64425
SylowC72 ⋊ C2×C3×D5×C11
SylowC5 ⋊ C2×C11×#64425

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊#64425
commutator, cosocle, hypocenterC5×C72C22×C3×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C2×C11

200 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 52 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

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 501);