Finite Group Databasebeta

← Prev (#36268483) Next (#36268485) →

C4×#19128497 #36268484

order21248
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#19128497

Splittings

FittingC4×AGL(1,ℤ/8)×C83 ⋊ C2
SylowC83 ⋊ C4×#575

Subgroups

subgroupG/H
centerC2×C4C2×D4×D83
commutatorC4×C83C24×C4
FrattiniC2×C4C24×D83
FittingC4×AGL(1,ℤ/8)×C83C2
socleC22×C83C23×D4
prime radicalC2×#19128497C2
cosocleC2×C4×C83C25
hypercenterC4×AGL(1,ℤ/8)D83
hypocenterC83C4×#575
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1033648);