Finite Group Databasebeta

SD16×D769 #37589911

order24608
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD16×D769

Splittings

FittingSD16×C769 ⋊ C2
SylowC769 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC2D4×D769
commutator, cosocleC4×C769C23
FrattiniC4C22×D769
FittingSD16×C769C2
socleC2×C769C2×D4
prime radicalD4×D769C2
hypercenterSD16D769
hypocenterC769C2×SD16
LCSG ▷ C4×C769 ▷ C2×C769 ▷ C769
UCSC1 ◁ C2 ◁ C4 ◁ SD16

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6152

Conjugacy classes & character table

2702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24608, 158);