Finite Group Databasebeta

C2×#24912582 #35574544

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

Aliases

direct productC2×#24912582

Splittings

SylowC83 ⋊ C2×#2558

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#390×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
hypercenterC2×#390D83
hypocenterC83C2×#2558
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#390

2834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

2372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 339708);