Finite Group Databasebeta

C2×#24909039 #35434370

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

Aliases

direct productC2×#24909039

Splittings

SylowC83 ⋊ C2×#2102

Subgroups

subgroupG/H
centerC2×C4#14581780
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×H(3,ℤ/4)×C83C2
socleC22×C83#400
prime radicalC24×C83#41
hypercenterC2×H(3,ℤ/4)D83
hypocenterC83C2×#2102
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 199534);