Finite Group Databasebeta

C22×C8×C22⋊D79 #35152099

order20224
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C8×C22⋊D79

Splittings

FittingC24×C8×C79 ⋊ C2
SylowC79 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C8C2×D79
commutatorC2×C79C24×C8
FrattiniC2×C4C24×D79
FittingC24×C8×C79C2
socleC24×C79C22×C4
prime radicalC23×C22⋊D79C4
cosocleC2×C4×C79C25
hypercenterC24×C8D79
hypocenterC79C22×C8×D4
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C23×C8 ◁ C24×C8

3694 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, 1033398);