Finite Group Databasebeta

C2×#13124300 #16729749

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13124300

Splittings

FittingC22×C4×D4×C13 ⋊ C2
SylowC13 ⋊ C2×#3036

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C4×D4×C13C2
socleC23×C13C22×D4
hypercenterC22×C4×D4D13
hypocenterC13C2×#3036
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036398);