Finite Group Databasebeta

C2×#28408866 #44402026

order29056
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28408866

Splittings

SylowC227 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D227
commutatorC2×C227C22×C16
FrattiniC16C22×D227
FittingC22×C16×C227C2
socleC22×C227C2×C16
prime radicalC23×C227C16
cosocleC16×C227C23
hypercenterC22×C16D227
hypocenterC227C2×M64
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C16 ◁ C22×C16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6802);