Finite Group Databasebeta

#391×D227 #44402200

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#391×D227

Splittings

Fitting#391×C227 ⋊ C2
SylowC227 ⋊ C2×#391

Subgroups

subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
Fitting#391×C227C2
socle, cosocleC23×C227C24
prime radicalC23×D227C23
hypercenter#391D227
hypocenterC227C2×#391
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ #391

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6976);