Finite Group Databasebeta

#431×D227 #44408346

order29056
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#431×D227

Splittings

Fitting#431×C227 ⋊ C2
SylowC227 ⋊ C2×#431

Subgroups

subgroupG/H
centerC42C22×D227
commutatorC2×C227C23×C8
FrattiniC2×C4C23×D227
Fitting#431×C227C2
socleC22×C227C23×C4
prime radicalC23×D227C2×C4
cosocleC2×C4×C227C24
hypercenter#431D227
hypocenterC227C2×#431
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C42 ◁ #431

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13122);