Finite Group Databasebeta

C2×#13123946 #16727965

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123946

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ C2×#2988

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC2×C13C24×C8
FrattiniC2×C4C24×D13
FittingC2×C8×Q8×C13C2
socleC23×C13C23×C4
prime radicalC22×#6131C4
cosocleC2×C4×C13C25
hypercenterC2×C8×Q8D13
hypocenterC13C2×#2988
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1034614);