Finite Group Databasebeta

C2×#26018546 #36520045

order22784
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8

Aliases

direct productC2×#26018546

Splittings

FittingC2×C82×C89 ⋊ C2
SylowC89 ⋊ C2×#1453

Subgroups

subgroupG/H
centerC2×C42C22×D89
commutatorC22×C89C22×C42
FrattiniC42C23×D89
FittingC2×C82×C89C2
socleC23×C89C2×C42
prime radicalC23×D89C42
cosocleC42×C89C24
hypercenterC2×C82D89
hypocenterC89C2×#1453
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C2×C42 ◁ C2×C82

866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11392

Conjugacy classes & character table

5744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 135185);