Finite Group Databasebeta

C22×#19099329 #35202033

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

Aliases

direct productC22×#19099329

Splittings

FittingC23×M16×C79 ⋊ C2
SylowC79 ⋊ C22×#568

Subgroups

subgroupG/H
centerC22×C4C23×D79
commutatorC2×C79C25×C4
FrattiniC4C25×D79
FittingC23×M16×C79C2
socleC23×C79C23×C4
prime radicalC23×#11929624C2
cosocleC4×C79C26
hypercenterC23×M16D79
hypocenterC79C22×#568
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C23×M16

11118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1083332);