Finite Group Databasebeta

C2×#13093016 #15686750

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

Aliases

direct productC2×#13093016

Splittings

FittingC2×C23×C22⋊Q8 ⋊ C2
SylowC23 ⋊ C2×#539

Subgroups

subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC2×C23×C22⋊Q8C2
socleC23×C23C24
prime radicalC2×#10625101C2
hypercenterC2×C22⋊Q8D23
hypocenterC23C2×#539
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17863);