Finite Group Databasebeta

C2×D656 #14580757

order2624
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D656

Splittings

FittingC2×C16×C41 ⋊ C2
SylowC41 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22D328
commutator, cosocleC8×C41C23
FrattiniC8C22×D41
FittingC2×C16×C41C2
socleC22×C41D8
hypercenterC2×C16D41
hypocenterC41C2×D16
LCSG ▷ C8×C41 ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 970);