Finite Group Databasebeta

C2×#24908460 #35431187

order21248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×#24908460

Splittings

FittingC22×#102×C83 ⋊ C2
SylowC83 ⋊ C2×#1999

Subgroups

subgroupG/H
centerC24D4×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC22×#102×C83C2
socleC24×C83C2×D4
hypercenterC22×#102D83
hypocenterC83C2×#1999
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

2870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

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, 196351);