Finite Group Databasebeta

C2×#13092951 #15686663

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

Aliases

direct productC2×#13092951

Splittings

FittingC22×C42×C23 ⋊ C2
SylowC23 ⋊ C2×#529

Subgroups

subgroupG/H
centerC22×C4C22×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC22×C42×C23C2
socleC23×C23C24
prime radicalC2×#10625101C2
hypercenterC22×C42D23
hypocenterC23C2×#529
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C22×C42

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17776);