Finite Group Databasebeta

C4×#20300271 #44402256

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

Aliases

direct productC4×#20300271

Splittings

FittingC22×C42×C227 ⋊ C2
SylowC227 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC22×C227C23×C4
FrattiniC23C23×D227
FittingC22×C42×C227C2
socle, cosocleC23×C227C24
prime radicalC22×C22⋊D227C22
hypercenterC22×C42D227
hypocenterC227C4×#123
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C22×C42

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 7032);