Finite Group Databasebeta

C2×#13113742 #15832680

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13113742

Splittings

SylowC13 ⋊ C2×#1593

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×Q8⋊C8C2
socle, prime radicalC23×C13C4×D4
cosocleC42×C13C24
hypercenterC2×Q8⋊C8D13
hypocenterC13C2×#1593
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 139329);