Finite Group Databasebeta

C2×D7264 #44402032

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

Aliases

direct productC2×D7264

Splittings

FittingC2×C32×C227 ⋊ C2
SylowC227 ⋊ C2×D32

Subgroups

subgroupG/H
centerC22D3632
commutator, cosocleC16×C227C23
FrattiniC16C22×D227
FittingC2×C32×C227C2
socleC22×C227D16
hypercenterC2×C32D227
hypocenterC227C2×D32
LCSG ▷ C16×C227 ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6808);