Finite Group Databasebeta

#121×Dic281 #49097817

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

Aliases

direct product#121×Dic281

Splittings

SylowC281 ⋊ C4×#121

Subgroups

subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting, prime radicalC2×#121×C281C2
socle, cosocleC23×C281C24
hypercenterC2×#121D281
hypocenterC281C4×#121
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×#121

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

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, 7024);