Finite Group Databasebeta

C2×#13124151 #16729375

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13124151

Splittings

FittingC22×C13×2−1+4 ⋊ C2
SylowC13 ⋊ C2×#3013

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×2−1+4C2
socleC23×C13C22×D4
hypercenterC22×2−1+4D13
hypocenterC13C2×#3013
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×2−1+4

4782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036024);