Finite Group Databasebeta

M16×Dic218 #28371985

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic218

Splittings

SylowC109 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D109
commutator, socleC22×C109C23×C4
FittingC4×M16×C109C2
prime radicalC23×C109C22×C4
cosocleC2×C4×C109C24
hypercenterC4×M16D109
hypocenterC109Q8×M16
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13463);