Finite Group Databasebeta

C2×#23761636 #34209403

order20224
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#23761636

Splittings

FittingC22×#95×C79 ⋊ C2
SylowC79 ⋊ C2×#1437

Subgroups

subgroupG/H
centerC25C22×D79
commutatorC22×C79C22×C42
FrattiniC24C23×D79
FittingC22×#95×C79C2
socleC25×C79C23
prime radicalC25×D79C22
cosocleC24×C79C24
hypercenterC22×#95D79
hypocenterC79C2×#1437
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C25 ◁ C22×#95

5230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

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, 90702);