Finite Group Databasebeta

#388×D281 #49097731

order35968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#388×D281

Splittings

Fitting#388×C281 ⋊ C2
SylowC281 ⋊ C2×#388

Subgroups

subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#388×C281C2
socle, cosocleC23×C281C24
prime radicalC24×D281C22
hypercenter#388D281
hypocenterC281C2×#388
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #388

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

3976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6938);