Finite Group Databasebeta

#443×D227 #44408620

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

Aliases

direct product#443×D227

Splittings

Fitting#443×C227 ⋊ C2
SylowC227 ⋊ C2×#443

Subgroups

subgroupG/H
centerC8D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
Fitting#443×C227C2
socleC2×C227C2×C4×D4
prime radical#135×D227C2
cosocleC2×C4×C227C24
hypercenter#443D227
hypocenterC227C2×#443
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C8 ◁ C2×C8 ◁ #443

472 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, 13396);