Finite Group Databasebeta

C4×#20300244 #44402072

order29056
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#20300244

Splittings

SylowC227 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC2×C227C22×C42
FrattiniC23C23×D227
FittingC4×C22⋊C4×C227C2
socle, cosocleC23×C227C24
prime radicalC24×C227C23
hypercenterC4×C22⋊C4D227
hypocenterC227C4×#117
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

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, 6848);