Finite Group Databasebeta

#461×D227 #44409148

order29056
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#461×D227

Splittings

Fitting#461×C227 ⋊ C2
SylowC227 ⋊ C2×#461

Subgroups

subgroupG/H
centerC22C2×D4×D227
commutator, cosocleC2×C4×C227C24
FrattiniC2×C4C23×D227
Fitting#461×C227C2
socleC22×C227C22×D4
prime radicalC2×D4×D227C22
hypercenter#461D227
hypocenterC227C2×#461
LCSG ▷ C2×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ #461

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

2185 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13924);