Finite Group Databasebeta

C2×#13092353 #15676645

order2944
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13092353

Splittings

SylowC23 ⋊ C2×#399

Subgroups

subgroupG/H
centerC24C22×D23
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC22×C22⋊C4×C23C2
socleC24×C23C23
prime radicalC25×C23C22
hypercenterC22×C22⋊C4D23
hypocenterC23C2×#399
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 261 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) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7758);