Finite Group Databasebeta

C2×#23765010 #34440937

order20224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23765010

Splittings

FittingC22×M32×C79 ⋊ C2
SylowC79 ⋊ C2×#2112

Subgroups

subgroupG/H
centerC22×C8C22×D79
commutatorC22×C79C23×C8
FrattiniC2×C8C23×D79
FittingC22×M32×C79C2
socleC23×C79C22×C8
prime radicalC24×D79C8
cosocleC2×C8×C79C24
hypercenterC22×M32D79
hypocenterC79C2×#2112
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C8 ◁ C22×M32

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 322236);