Finite Group Databasebeta

C22⋊C8×#1055 #15753386

order3328
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC22⋊C8×#1055

Splittings

SylowC13 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C42C22×D13
commutatorC2×C13C2×C82
FittingC4×C13×C22⋊C8C2
socleC23×C13C2×C42
prime radicalC24×C13C42
cosocleC2×C42×C13C23
hypercenterC4×C22⋊C8D13
hypocenterC13C8×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 60035);