Finite Group Databasebeta

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C4×#19151769 #36560320

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

Aliases

direct productC4×#19151769

Splittings

FittingC4×AGL(1,ℤ/8)×C89 ⋊ C2
SylowC89 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#15667980
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingC4×AGL(1,ℤ/8)×C89C2
socleC22×C89C2×#120
prime radicalC2×#19151769C2
cosocleC22×C4×C89C24
hypercenterC4×AGL(1,ℤ/8)D89
hypocenterC89C4×#454
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 175460);