Finite Group Databasebeta

SD16⋊C8×D67 #30825212

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productSD16⋊C8×D67

Splittings

FittingC67×SD16⋊C8 ⋊ C2
SylowC67 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutatorC4×C67C23×C8
FrattiniC42C23×D67
FittingC67×SD16⋊C8C2
socleC22×C67C2×C4×D4
prime radicalC2×D4×D67C2×C4
cosocleC42×C67C24
hypercenterSD16⋊C8D67
hypocenterC67C2×SD16⋊C8
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 138949);