Finite Group Databasebeta

C2×#13092332 #15676601

order2944
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13092332

Splittings

FittingC22×C22⋊C4×C23 ⋊ C2
SylowC23 ⋊ C2×#394

Subgroups

subgroupG/H
centerC24C22×D23
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC22×C22⋊C4×C23C2
socleC24×C23C23
prime radicalC23×C22⋊D23C2
hypercenterC22×C22⋊C4D23
hypocenterC23C2×#394
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

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, 7714);