Finite Group Databasebeta

C2×#24908783 #35432344

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

Aliases

direct productC2×#24908783

Splittings

SylowC83 ⋊ C2×#2056

Subgroups

subgroupG/H
centerC24D4×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC23×Q16×C83C2
socle, prime radicalC24×C83C2×D4
hypercenterC23×Q16D83
hypocenterC83C2×#2056
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q16

1486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 197508);