Finite Group Databasebeta

C8×M16×D13 #15828489

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×M16×D13

Splittings

FittingC8×C13×M16 ⋊ C2
SylowC13 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC4×C8C22×D13
commutatorC2×C13C22×C4×C8
FrattiniC42C23×D13
FittingC8×C13×M16C2
socleC22×C13C22×C42
prime radicalC23×D13C42
cosocleC42×C13C24
hypercenterC8×M16D13
hypocenterC13C2×C8×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C8×M16

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135138);