Finite Group Databasebeta

M16×Dic46 #15682350

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic46

Splittings

SylowC23 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D23
commutator, socleC22×C23C23×C4
FittingC4×M16×C23C2
prime radicalC23×C23C22×C4
cosocleC2×C4×C23C24
hypercenterC4×M16D23
hypocenterC23Q8×M16
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13463);