Finite Group Databasebeta

#340×Dic89 #36459607

order22784
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct product#340×Dic89

Splittings

SylowC89 ⋊ C4×#340

Subgroups

subgroupG/H
centerC24D4×D89
commutatorC4×C89C43
FrattiniC23×C4C22×D89
FittingC2×#340×C89C2
socle, prime radicalC24×C89C2×D4
cosocleC23×C4×C89C23
hypercenterC2×#340D89
hypocenterC89C4×#340
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

2576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 74747);