Finite Group Databasebeta

C22×C4×#11929624 #35194843

order20224
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×C4×#11929624

Splittings

FittingC23×C42×C79 ⋊ C2
SylowC79 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC22×C42C2×D79
commutatorC2×C79C25×C4
FrattiniC22C25×D79
FittingC23×C42×C79C2
socleC24×C79C24
prime radicalC23×#11929624C2
cosocleC22×C79C26
hypercenterC23×C42D79
hypocenterC79C22×C4×#41
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C42 ◁ C23×C42

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

5152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1076142);