Finite Group Databasebeta

C22×(C2×D79)⋊C16 #34440933

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

Aliases

direct productC22×(C2×D79)⋊C16

Splittings

FittingC23×C16×C79 ⋊ C2
SylowC79 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D79
commutatorC2×C79C23×C16
FrattiniC2×C8C23×D79
FittingC23×C16×C79C2
socleC24×C79C2×C8
prime radicalC24×D79C8
cosocleC2×C8×C79C24
hypercenterC23×C16D79
hypocenterC79C22×C22⋊C16
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C23×C8 ◁ C23×C16

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, 322232);