Finite Group Databasebeta

C2×#28408791 #44399439

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

Aliases

direct productC2×#28408791

Splittings

SylowC227 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4C22⋊D227
commutatorC4×C227C2×C42
FrattiniC22×C4C22×D227
FittingC2×#117×C227C2
socleC23×C227C22⋊C4
prime radicalC24×C227D4
cosocleC22×C4×C227C23
hypercenterC2×#117D227
hypocenterC227C2×#339
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

488 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, 4215);