Finite Group Databasebeta

C4×#19151601 #36552202

order22784
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#19151601

Splittings

FittingC4×#102×C89 ⋊ C2
SylowC89 ⋊ C4×#418

Subgroups

subgroupG/H
centerC22×C4D4×D89
commutatorC4×C89C22×C42
FrattiniC22×C4C23×D89
FittingC4×#102×C89C2
socleC23×C89C22×D4
prime radicalC22×D4×D89C22
cosocleC22×C4×C89C24
hypercenterC4×#102D89
hypocenterC89C4×#418
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 167342);