Finite Group Databasebeta

#383×D257 #45666708

order32896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#383×D257

Splittings

Fitting#383×C257 ⋊ C2
SylowC257 ⋊ C2×#383

Subgroups

subgroupG/H
center, FrattiniC23C23×D257
commutatorC22×C257C23×C4
Fitting#383×C257C2
socle, cosocleC23×C257C24
prime radicalC23×D257C23
hypercenter#383D257
hypocenterC257C2×#383
LCSG ▷ C22×C257 ▷ C257
UCSC1 ◁ C23 ◁ #383

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16448

Conjugacy classes & character table

3640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 6898);