Finite Group Databasebeta

C8×SD16×D73 #33055343

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×SD16×D73

Splittings

FittingC8×SD16×C73 ⋊ C2
SylowC73 ⋊ C2×C8×SD16

Subgroups

subgroupG/H
centerC2×C8D4×D73
commutatorC4×C73C23×C8
FrattiniC42C23×D73
FittingC8×SD16×C73C2
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C2×C4
cosocleC42×C73C24
hypercenterC8×SD16D73
hypocenterC73C2×C8×SD16
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×SD16

822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 138927);