Finite Group Databasebeta

M16×#11924015 #33057424

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×#11924015

Splittings

FittingQ8×M16×C73 ⋊ C2
SylowC73 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingQ8×M16×C73C2
socleC22×C73C2×C4×D4
prime radicalC22×D292C2×C4
cosocleC42×C73C24
hypercenterQ8×M16D73
hypocenterC73M16×SD16
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ Q8×M16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 141008);