Finite Group Databasebeta

C2×#13093014 #15686748

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

Aliases

direct productC2×#13093014

Splittings

FittingC22×C4⋊C4×C23 ⋊ C2
SylowC23 ⋊ C2×#539

Subgroups

subgroupG/H
centerC23C23×D23
commutator, cosocleC22×C23C25
FrattiniC22C24×D23
FittingC22×C4⋊C4×C23C2
socleC23×C23C24
prime radicalC2×#10625101C2
hypercenterC22×C4⋊C4D23
hypocenterC23C2×#539
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4⋊C4

1144 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, 17861);