Finite Group Databasebeta

SD16×#11761612 #30827272

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productSD16×#11761612

Splittings

SylowC67 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC42C23×D67
FittingC2×C4×SD16×C67C2
socleC22×C67C2×C4×D4
prime radicalC22×D4×C67C2×C4
cosocleC42×C67C24
hypercenterC2×C4×SD16D67
hypocenterC67M16×SD16
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×SD16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1918 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 141009);