Finite Group Databasebeta

M16×D664 #35375828

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×D664

Splittings

FittingC8×M16×C83 ⋊ C2
SylowC83 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC8×M16×C83C2
socleC22×C83C2×C4×D4
prime radicalC22×D664C4
cosocleC42×C83C24
hypercenterC8×M16D83
hypocenterC83M16×D8
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 140992);