Finite Group Databasebeta

C4×#19151657 #36552573

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

Aliases

direct productC4×#19151657

Splittings

FittingC42×C8×C89 ⋊ C2
SylowC89 ⋊ C4×#433

Subgroups

subgroupG/H
centerC2×C42C22×D89
commutatorC22×C89C22×C42
FrattiniC22×C4C23×D89
FittingC42×C8×C89C2
socleC23×C89C23×C4
prime radicalC23×D89C22×C4
cosocleC22×C4×C89C24
hypercenterC42×C8D89
hypocenterC89C4×#433
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C2×C42 ◁ C42×C8

970 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, 167713);