Finite Group Databasebeta

M16×Dic538 #46819838

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic538

Splittings

SylowC269 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D269
commutator, socleC22×C269C23×C4
FittingC4×M16×C269C2
prime radicalC23×C269C22×C4
cosocleC2×C4×C269C24
hypercenterC4×M16D269
hypocenterC269Q8×M16
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

5410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 13463);