Finite Group Databasebeta

C2×#24913051 #35575787

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

Aliases

direct productC2×#24913051

Splittings

FittingC2×#397×C83 ⋊ C2
SylowC83 ⋊ C2×#2600

Subgroups

subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#397×C83C2
socleC24×C83C24
prime radicalC2×#19127610C2
hypercenterC2×#397D83
hypocenterC83C2×#2600
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#397

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 340951);