Finite Group Databasebeta

M16×Dic58 #16828445

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic58

Splittings

SylowC29 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D29
commutator, socleC22×C29C23×C4
FittingC4×M16×C29C2
prime radicalC23×C29C22×C4
cosocleC2×C4×C29C24
hypercenterC4×M16D29
hypocenterC29Q8×M16
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13463);