Finite Group Databasebeta

#344×D281 #49095043

order35968
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D281

Splittings

Fitting#344×C281 ⋊ C2
SylowC281 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D281
commutatorC22×C281C2×C42
FrattiniC22×C4C22×D281
Fitting#344×C281C2
socleC2×C281C2×#95
prime radicalC23×D281C2×C4
cosocleC22×C4×C281C23
hypercenter#344D281
hypocenterC281C2×#344
LCSG ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4496

Conjugacy classes & character table

3124 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 4250);