Finite Group Databasebeta

C22×D368 #15686503

order2944
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×D368

Splittings

FittingC22×C16×C23 ⋊ C2
SylowC23 ⋊ C22×D16

Subgroups

subgroupG/H
centerC23D184
commutator, cosocleC8×C23C24
FrattiniC8C23×D23
FittingC22×C16×C23C2
socleC23×C23D8
hypercenterC22×C16D23
hypocenterC23C22×D16
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17616);