Finite Group Databasebeta

M16×Dic254 #30647683

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic254

Splittings

SylowC127 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D127
commutator, socleC22×C127C23×C4
FittingC4×M16×C127C2
prime radicalC23×C127C22×C4
cosocleC2×C4×C127C24
hypercenterC4×M16D127
hypocenterC127Q8×M16
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13463);