Finite Group Databasebeta

C2×#30659648 #45687847

order33344
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30659648

Splittings

SylowC521 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D521
commutatorC2×C521C22×C8
FrattiniC8C22×D521
FittingC22×C8×C521C2
socleC22×C521C2×C8
prime radicalC23×C521C8
cosocleC8×C521C23
hypercenterC22×C8D521
hypocenterC521C2×M32
LCSG ▷ C2×C521 ▷ C521
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16672

Conjugacy classes & character table

8360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33344, 964);