Finite Group Databasebeta

C2×#13112787 #15772104

order3328
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13112787

Splittings

SylowC13 ⋊ C2×#1327

Subgroups

subgroupG/H
centerC2×C4#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×M16C22×D13
FittingC2×C13×#423C2
socleC22×C13#324
prime radicalC24×C13M16
cosocleC2×C13×M16C23
hypercenterC2×#423D13
hypocenterC13C2×#1327
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#423

410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 78753);