Finite Group Databasebeta

C2×#28408994 #44408168

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

Aliases

direct productC2×#28408994

Splittings

FittingC2×C22⋊C8×C227 ⋊ C2
SylowC227 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC22×C227C23×C4
FrattiniC2×C4C23×D227
FittingC2×C22⋊C8×C227C2
socleC23×C227C22×C4
prime radicalC24×D227C4
cosocleC2×C4×C227C24
hypercenterC2×C22⋊C8D227
hypocenterC227C2×#407
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

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, 12944);