Finite Group Databasebeta

#101×C22⋊D89 #36569795

order22784
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#101×C22⋊D89

Splittings

FittingC22×#101×C89 ⋊ C2
SylowC89 ⋊ D4×#101

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D89
commutatorC23×C89C23×C4
FrattiniC22×C4C23×D89
FittingC22×#101×C89C2
socleC22×C89C22×C22⋊C4
prime radicalC22×C22⋊D89C2×C4
cosocleC22×C4×C89C24
hypercenterC22×#101D89
hypocenterC89D4×#101
LCSG ▷ C23×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

1378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

1991 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 184935);