Finite Group Databasebeta

C2×#28408996 #44408170

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

Aliases

direct productC2×#28408996

Splittings

SylowC227 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC22×C227C23×C4
FrattiniC2×C4C23×D227
FittingC24×C4×C227C2
socleC23×C227C22×C4
prime radicalC25×C227C4
cosocleC2×C4×C227C24
hypercenterC24×C4D227
hypocenterC227C2×#407
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C24×C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

7288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 12946);