Finite Group Databasebeta

#400×Dic89 #36476278

order22784
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#400×Dic89

Splittings

SylowC89 ⋊ C4×#400

Subgroups

subgroupG/H
center, FrattiniC24C23×D89
commutatorC23×C89C23×C4
FittingC2×#400×C89C2
socle, prime radical, cosocleC24×C89C24
hypercenterC2×#400D89
hypocenterC89C4×#400
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#400

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 91418);