Finite Group Databasebeta

C2×#13093135 #15686941

order2944
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13093135

Splittings

FittingC2×C23×#117 ⋊ C2
SylowC23 ⋊ C2×#556

Subgroups

subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC2×C23×#117C2
socleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenterC2×#117D23
hypocenterC23C2×#556
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×#117

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 18054);