Finite Group Databasebeta

C22×C22⋊(C79⋊C16) #34440934

order20224
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊(C79⋊C16)

Splittings

SylowC79 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D79
commutatorC2×C79C23×C16
FrattiniC2×C8C23×D79
FittingC24×C8×C79C2
socleC24×C79C2×C8
prime radicalC25×C79C8
cosocleC2×C8×C79C24
hypercenterC24×C8D79
hypocenterC79C22×C22⋊C16
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C23×C8 ◁ C24×C8

1470 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, 322233);