Finite Group Databasebeta

C2×#28408932 #44402188

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#28408932

Splittings

FittingC22×C22⋊C4×C227 ⋊ C2
SylowC227 ⋊ C2×#390

Subgroups

subgroupG/H
centerC24C22×D227
commutatorC22×C227C23×C4
FrattiniC23C23×D227
FittingC22×C22⋊C4×C227C2
socleC24×C227C23
prime radicalC23×C22⋊D227C2
cosocleC23×C227C24
hypercenterC22×C22⋊C4D227
hypocenterC227C2×#390
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6964);