Finite Group Databasebeta

C2×#13113095 #15784608

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13113095

Splittings

SylowC13 ⋊ C2×#1442

Subgroups

subgroupG/H
centerC25C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC23×C13×C4⋊C4C2
socle, prime radicalC25×C13C23
cosocleC24×C13C24
hypercenterC23×C4⋊C4D13
hypocenterC13C2×#1442
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C25 ◁ C23×C4⋊C4

2942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91257);