Finite Group Databasebeta

C2×#24908891 #35433237

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

Aliases

direct productC2×#24908891

Splittings

SylowC83 ⋊ C2×#2076

Subgroups

subgroupG/H
centerC24C2×D332
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC22×C22⋊C8×C83C2
socleC24×C83C2×D4
prime radicalC25×C83D4
hypercenterC22×C22⋊C8D83
hypocenterC83C2×#2076
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 198401);