Finite Group Databasebeta

C22×#95×D89 #36712594

order22784
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C212

Aliases

direct productC22×#95×D89

Splittings

FittingC22×#95×C89 ⋊ C2
SylowC89 ⋊ C23×#95

Subgroups

subgroupG/H
centerC25C22×D89
commutatorC2×C89C23×C42
FrattiniC23C24×D89
FittingC22×#95×C89C2
socleC25×C89C23
prime radicalC25×D89C22
cosocleC23×C89C25
hypercenterC22×#95D89
hypocenterC89C23×#95
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C25 ◁ C22×#95

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11392

Conjugacy classes & character table

3680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 327734);