Finite Group Databasebeta

#432×D227 #44408351

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

Aliases

direct product#432×D227

Splittings

Fitting#432×C227 ⋊ C2
SylowC227 ⋊ C2×#432

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D227
commutator, socleC22×C227C23×C4
Fitting#432×C227C2
prime radicalC23×D227C2×C4
cosocleC2×C4×C227C24
hypercenter#432D227
hypocenterC227C2×#432
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ #432

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

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, 13127);