Finite Group Databasebeta

#344×D227 #44399474

order29056
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D227

Splittings

Fitting#344×C227 ⋊ C2
SylowC227 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D227
commutatorC22×C227C2×C42
FrattiniC22×C4C22×D227
Fitting#344×C227C2
socleC2×C227C2×#95
prime radicalC23×D227C2×C4
cosocleC22×C4×C227C23
hypercenter#344D227
hypocenterC227C2×#344
LCSG ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3632

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, 4250);