Finite Group Databasebeta

C2×#24920507 #36285386

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#24920507

Splittings

FittingC2×#446×C83 ⋊ C2
SylowC83 ⋊ C2×#3399

Subgroups

subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#446×C83C2
socleC23×C83C22×D4
hypercenterC2×#446D83
hypocenterC83C2×#3399
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

2314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1050550);