Finite Group Databasebeta

C2×#28408955 #44402955

order29056
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#28408955

Splittings

SylowC227 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D227
commutator, cosocleC23×C227C24
FrattiniC23C23×D227
FittingC22×C22⋊C4×C227C2
socleC24×C227C23
prime radicalC25×C227C22
hypercenterC22×C22⋊C4D227
hypocenterC227C2×#396
LCSG ▷ C23×C227 ▷ C227
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 7731);