Finite Group Databasebeta

C2×#24909046 #35434384

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

Aliases

direct productC2×#24909046

Splittings

SylowC83 ⋊ C2×#2103

Subgroups

subgroupG/H
centerC2×C4#14581778
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×#344×C83C2
socleC22×C83#400
prime radicalC24×C83C2×Q8
hypercenterC2×#344D83
hypocenterC83C2×#2103
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

662 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, 199548);