Finite Group Databasebeta

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C2×C11⋊C5×#64418 #44568566

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

Aliases

direct productC2×C11⋊C5×#64418
unambiguous semidirect product(C2×C11×#64418)⋊C5

Splittings

Fitting, socleC2×C72×C11 ⋊ C5×D3
derived, HallC11×#3862 ⋊ C22×C5
HallC11⋊C5×#3862 ⋊ C22
HallC2×C11×#64418 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×D3
HallC72×C11 ⋊ C2×C5×D3
Hall#3862 ⋊ C22×C11⋊C5
SylowC72 ⋊ C2×D3×C11⋊C5
SylowC11 ⋊ C2×C5×#64418

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×#64418
commutator, cosocle, hypocenterC11×#3862C22×C5
FrattiniC1G
Fitting, socleC2×C72×C11C5×D3
LCSG ▷ C11×#3862
UCSC1 ◁ C2

136 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 27 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) = 308

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 268);