Finite Group Databasebeta

C2×#24906959 #35386922

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

Aliases

direct productC2×#24906959

Splittings

FittingC2×#498×C83 ⋊ C2
SylowC83 ⋊ C2×#1691

Subgroups

subgroupG/H
centerC23#14581763
commutator, cosocleC42×C83C24
FrattiniC42C23×D83
FittingC2×#498×C83C2
socleC23×C83#121
prime radicalC22×D332D4
hypercenterC2×#498D83
hypocenterC83C2×#1691
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 152086);