Finite Group Databasebeta

C2×#13125708 #16733594

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13125708

Splittings

SylowC13 ⋊ C2×#3200

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#535C2
socleC23×C13C22×D4
hypercenterC2×#535D13
hypocenterC13C2×#3200
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

2314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1040243);