Finite Group Databasebeta

C2×#24908758 #35432274

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

Aliases

direct productC2×#24908758

Splittings

FittingC2×#343×C83 ⋊ C2
SylowC83 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#14581765
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×#343×C83C2
socleC23×C83#121
prime radicalC22×#14581820C2
hypercenterC2×#343D83
hypocenterC83C2×#2051
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 197438);