Finite Group Databasebeta

#137×Dic227 #44408555

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

Aliases

direct product#137×Dic227

Splittings

SylowC227 ⋊ C4×#137

Subgroups

subgroupG/H
centerC22C2×D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC2×#137×C227C2
socleC22×C227C22×D4
prime radicalC2×#41×C227C22
cosocleC2×C4×C227C24
hypercenterC2×#137D227
hypocenterC227C4×#137
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

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, 13331);