Finite Group Databasebeta

#102×C22⋊D89 #36569830

order22784
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#102×C22⋊D89

Splittings

FittingC22×#102×C89 ⋊ C2
SylowC89 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C2×D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC22×#102×C89C2
socleC23×C89C22×D4
prime radicalC2×D4×C22⋊D89C2
cosocleC22×C4×C89C24
hypercenterC22×#102D89
hypocenterC89D4×#102
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2534 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 184970);