Finite Group Databasebeta

#428×D227 #44408315

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

Aliases

direct product#428×D227

Splittings

Fitting#428×C227 ⋊ C2
SylowC227 ⋊ C2×#428

Subgroups

subgroupG/H
centerC22C2×D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
Fitting#428×C227C2
socleC22×C227C22×D4
prime radicalC23×D227D4
cosocleC2×C4×C227C24
hypercenter#428D227
hypocenterC227C2×#428
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13091);