Finite Group Databasebeta

C22×#19098298 #34255348

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#19098298

Splittings

FittingC22×C22⋊C8×C79 ⋊ C2
SylowC79 ⋊ C22×#327

Subgroups

subgroupG/H
centerC24(C2×D79)⋊C4
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC22×C22⋊C8×C79C2
socleC24×C79C22⋊C4
prime radicalC22×#14579135C2
cosocleC22×C4×C79C24
hypercenterC22×C22⋊C8D79
hypocenterC79C22×#327
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 136647);