Finite Group Databasebeta

C2×#24921160 #36312457

order21248
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#24921160

Splittings

SylowC83 ⋊ C2×#3491

Subgroups

subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
Fitting, prime radicalC2×#534×C83C2
socleC23×C83C25
hypercenterC2×#534D83
hypocenterC83C2×#3491
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#534

7390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1077621);