Finite Group Databasebeta

C2×C4×M16×D13 #16726303

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

Aliases

direct productC2×C4×M16×D13

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC2×C4×C13×M16C2
socleC23×C13C23×C4
prime radicalC24×D13C2×C4
cosocleC2×C4×C13C25
hypercenterC2×C4×M16D13
hypocenterC13C22×C4×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3950 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, 1032952);