Finite Group Databasebeta

C2×#23764577 #34315707

order20224
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23764577

Splittings

SylowC79 ⋊ C2×#2032

Subgroups

subgroupG/H
centerC22#19098475
commutator, cosocleC24×C79C24
FrattiniC24C23×D79
FittingC22×#99×C79C2
socleC22×C79#393
prime radicalC23×D4×C79C22
hypercenterC22×#99D79
hypocenterC79C2×#2032
LCSG ▷ C24×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2528

Conjugacy classes & character table

1762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 197006);