Finite Group Databasebeta

C2×#28408802 #44399475

order29056
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28408802

Splittings

SylowC227 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4(C2×D227)⋊C4
commutatorC22×C227C2×C42
FrattiniC22×C4C22×D227
FittingC2×#117×C227C2
socleC22×C227#95
prime radicalC24×C227C2×C4
cosocleC22×C4×C227C23
hypercenterC2×#117D227
hypocenterC227C2×#344
LCSG ▷ C22×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

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, 4251);