Finite Group Databasebeta

C2×M16×D52 #16726822

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×M16×D52

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×M16C2
socleC23×C13C23×C4
prime radicalC23×D52C4
cosocleC2×C4×C13C25
hypercenterC2×C4×M16D13
hypocenterC13C2×D4×M16
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033471);