Finite Group Databasebeta

SD16×D839 #41001569

order26848
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD16×D839

Splittings

FittingSD16×C839 ⋊ C2
SylowC839 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC2D4×D839
commutator, cosocleC4×C839C23
FrattiniC4C22×D839
FittingSD16×C839C2
socleC2×C839C2×D4
prime radicalD4×D839C2
hypercenterSD16D839
hypocenterC839C2×SD16
LCSG ▷ C4×C839 ▷ C2×C839 ▷ C839
UCSC1 ◁ C2 ◁ C4 ◁ SD16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6712

Conjugacy classes & character table

2947 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26848, 158);