Finite Group Databasebeta

C2×#24908984 #35434161

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

Aliases

direct productC2×#24908984

Splittings

SylowC83 ⋊ C2×#2092

Subgroups

subgroupG/H
centerC24C2×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC2×#390×C83C2
socleC24×C83C2×D4
prime radicalC23×D4×C83C22
hypercenterC2×#390D83
hypocenterC83C2×#2092
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

1366 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, 199325);