Finite Group Databasebeta

M16×Dic62 #16854664

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic62

Splittings

SylowC31 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D31
commutator, socleC22×C31C23×C4
FittingC4×M16×C31C2
prime radicalC23×C31C22×C4
cosocleC2×C4×C31C24
hypercenterC4×M16D31
hypocenterC31Q8×M16
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13463);