Finite Group Databasebeta

C2×#30659654 #45687859

order33344
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30659654

Splittings

SylowC521 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#22552349
commutator, cosocleC8×C521C23
FrattiniC8C22×D521
FittingC2×Q16×C521C2
socle, prime radicalC22×C521D8
hypercenterC2×Q16D521
hypocenterC521C2×Q32
LCSG ▷ C8×C521 ▷ C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33344

Conjugacy classes & character table

3662 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33344, 976);