Finite Group Databasebeta

C2×#13123254 #16726317

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#13123254

Splittings

SylowC13 ⋊ C2×#2873

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC23×C13×M16C2
socleC23×C13C23×C4
prime radicalC25×C13C2×C4
cosocleC2×C4×C13C25
hypercenterC23×M16D13
hypocenterC13C2×#2873
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×M16

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1032966);