Finite Group Databasebeta

M16×Dic454 #44408687

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic454

Splittings

SylowC227 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D227
commutator, socleC22×C227C23×C4
FittingC4×M16×C227C2
prime radicalC23×C227C22×C4
cosocleC2×C4×C227C24
hypercenterC4×M16D227
hypocenterC227Q8×M16
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13463);