Finite Group Databasebeta

C2×#26018371 #36469368

order22784
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#26018371

Splittings

SylowC89 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC23#15667926
commutatorC23×C89C2×C42
FrattiniC22×D4C22×D89
FittingC22×#100×C89C2
socleC23×C89#99
prime radicalC23×D4×C89C22
cosocleC22×D4×C89C23
hypercenterC22×#100D89
hypocenterC89C2×#1390
LCSG ▷ C23×C89 ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C22×#100

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84508);