Finite Group Databasebeta

#390×D281 #49097756

order35968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct product#390×D281

Splittings

Fitting#390×C281 ⋊ C2
SylowC281 ⋊ C2×#390

Subgroups

subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting#390×C281C2
socle, cosocleC23×C281C24
prime radicalC22×D4×D281C2
hypercenter#390D281
hypocenterC281C2×#390
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ #390

1360 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, 6963);