Finite Group Databasebeta

C2×#13113441 #15830830

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13113441

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C2×#1529

Subgroups

subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C4×C13×M16C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C4
cosocleC42×C13C24
hypercenterC2×C4×M16D13
hypocenterC13C2×#1529
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 137479);