Finite Group Databasebeta

C2×#26022299 #36708675

order22784
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#26022299

Splittings

SylowC89 ⋊ C2×#2209

Subgroups

subgroupG/H
centerC23C2×#13083559
commutator, cosocleC2×C8×C89C24
FrattiniC2×C8C23×D89
FittingC2×#494×C89C2
socle, prime radicalC23×C89C2×D8
hypercenterC2×#494D89
hypocenterC89C2×#2209
LCSG ▷ C2×C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#494

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

1994 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 323815);