Finite Group Databasebeta

C2×#24908742 #35432241

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

Aliases

direct productC2×#24908742

Splittings

FittingC22×#101×C83 ⋊ C2
SylowC83 ⋊ C2×#2049

Subgroups

subgroupG/H
centerC22#19127617
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC22×#101×C83C2
socleC22×C83#394
prime radicalC22×#13050590C22
hypercenterC22×#101D83
hypocenterC83C2×#2049
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

1322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 197405);