Finite Group Databasebeta

C2×#24909411 #35558290

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

Aliases

direct productC2×#24909411

Splittings

FittingC2×#349×C83 ⋊ C2
SylowC83 ⋊ C2×#2190

Subgroups

subgroupG/H
centerC22#19127837
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC2×#349×C83C2
socleC22×C83#447
hypercenterC2×#349D83
hypocenterC83C2×#2190
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

1180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 323454);