Finite Group Databasebeta

SD32×D379 #37565666

order24256
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productSD32×D379

Splittings

FittingSD32×C379 ⋊ C2
SylowC379 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC2D8×D379
commutator, cosocleC8×C379C23
FrattiniC8C22×D379
FittingSD32×C379C2
socleC2×C379C2×D8
prime radicalD8×D379C2
hypercenterSD32D379
hypocenterC379C2×SD32
LCSG ▷ C8×C379 ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6064

Conjugacy classes & character table

2101 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 971);