Finite Group Databasebeta

C2×C4×M16×D73 #33949368

order18688
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×M16×D73

Splittings

FittingC2×C4×M16×C73 ⋊ C2
SylowC73 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC2×C42C22×D73
commutatorC2×C73C23×C42
FrattiniC2×C4C24×D73
FittingC2×C4×M16×C73C2
socleC23×C73C23×C4
prime radicalC24×D73C2×C4
cosocleC2×C4×C73C25
hypercenterC2×C4×M16D73
hypocenterC73C22×C4×M16
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1032952);