Finite Group Databasebeta

SD16×(C2×D71)⋊C4 #32013279

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productSD16×(C2×D71)⋊C4

Splittings

FittingC2×C4×SD16×C71 ⋊ C2
SylowC71 ⋊ C22⋊C4×SD16

Subgroups

subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×C4×SD16×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
cosocleC22×C4×C71C24
hypercenterC2×C4×SD16D71
hypocenterC71C22⋊C4×SD16
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 185395);