Finite Group Databasebeta

C2×#24906426 #35376501

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

Aliases

direct productC2×#24906426

Splittings

SylowC83 ⋊ C2×#1603

Subgroups

subgroupG/H
centerC23#14581761
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×#539×C83C2
socleC23×C83#120
prime radicalC2×#121×C83C22
hypercenterC2×#539D83
hypocenterC83C2×#1603
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 141665);