Finite Group Databasebeta

C22×Q8×C22⋊D79 #35195183

order20224
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×Q8×C22⋊D79

Splittings

FittingC24×Q8×C79 ⋊ C2
SylowC79 ⋊ C22×D4×Q8

Subgroups

subgroupG/H
centerC24C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC24×Q8×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
hypercenterC24×Q8D79
hypocenterC79C22×D4×Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C24×Q8

11798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1076482);