Finite Group Databasebeta

C2×#28408911 #44402152

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#28408911

Splittings

FittingC24×C4×C227 ⋊ C2
SylowC227 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D227
commutatorC22×C227C23×C4
FrattiniC23C23×D227
FittingC24×C4×C227C2
socleC24×C227C23
prime radicalC23×C22⋊D227C2
cosocleC23×C227C24
hypercenterC24×C4D227
hypocenterC227C2×#386
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C24 ◁ C24×C4

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

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, 6928);