Finite Group Databasebeta

C2×#24906389 #35376490

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

Aliases

direct productC2×#24906389

Splittings

SylowC83 ⋊ C2×#1597

Subgroups

subgroupG/H
centerC23#14581760
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
Fitting, prime radicalC2×#447×C83C2
socleC23×C83#120
hypercenterC2×#447D83
hypocenterC83C2×#1597
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

1404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 141654);