Finite Group Databasebeta

C2×#30654161 #45655665

order32576
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30654161

Splittings

SylowC509 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#22550846
commutator, cosocleC8×C509C23
FrattiniC8C22×D509
FittingC2×Q16×C509C2
socle, prime radicalC22×C509D8
hypercenterC2×Q16D509
hypocenterC509C2×Q32
LCSG ▷ C8×C509 ▷ C4×C509 ▷ C2×C509 ▷ C509
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32576

Conjugacy classes & character table

3578 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 976);