Finite Group Databasebeta

C2×#13113147 #15828710

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13113147

Splittings

SylowC13 ⋊ C2×#1458

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC2×C13×#323C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC2×#323D13
hypocenterC13C2×#1458
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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(3328, 135359);