Finite Group Databasebeta

#339×D227 #44399438

order29056
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#339×D227

Splittings

Fitting#339×C227 ⋊ C2
SylowC227 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4D4×D227
commutatorC4×C227C2×C42
FrattiniC22×C4C22×D227
Fitting#339×C227C2
socleC22×C227C2×C22⋊C4
prime radicalC23×D227D4
cosocleC22×C4×C227C23
hypercenter#339D227
hypocenterC227C2×#339
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3632

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, 4214);