Finite Group Databasebeta

C2×#26023068 #36713596

order22784
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#26023068

Splittings

FittingC2×#379×C89 ⋊ C2
SylowC89 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#379×C89C2
socleC24×C89C24
prime radicalC24×C22⋊D89C2
cosocleC23×C89C25
hypercenterC2×#379D89
hypocenterC89C2×D4×C22⋊C4
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#379

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 328736);