Finite Group Databasebeta

C2×#24908749 #35432258

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#24908749

Splittings

FittingC22×#104×C83 ⋊ C2
SylowC83 ⋊ C2×#2050

Subgroups

subgroupG/H
centerC2×C4#14581778
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC22×#104×C83C2
socleC22×C83#394
prime radicalC2×#19128499C2
hypercenterC22×#104D83
hypocenterC83C2×#2050
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 197422);