Finite Group Databasebeta

#123×Dic281 #49097826

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

Aliases

direct product#123×Dic281

Splittings

SylowC281 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
FittingC2×#123×C281C2
socle, cosocleC23×C281C24
prime radicalC22×D4×C281C22
hypercenterC2×#123D281
hypocenterC281C4×#123
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×#123

688 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, 7033);