Finite Group Databasebeta

C2×#13113612 #15831981

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

Aliases

direct productC2×#13113612

Splittings

SylowC13 ⋊ C2×#1571

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#423C2
socleC23×C13C2×C4⋊C4
prime radicalC24×C13C4⋊C4
cosocleC42×C13C24
hypercenterC2×#423D13
hypocenterC13C2×#1571
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#423

770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 138630);