Finite Group Databasebeta

M16×D632 #34259693

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×D632

Splittings

FittingC8×M16×C79 ⋊ C2
SylowC79 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C22×D316
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC8×M16×C79C2
socleC22×C79C2×C4×D4
prime radicalC22×D632C4
cosocleC42×C79C24
hypercenterC8×M16D79
hypocenterC79M16×D8
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 140992);