Finite Group Databasebeta

C2×C4×M16×D79 #35151653

order20224
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×M16×D79

Splittings

FittingC2×C4×M16×C79 ⋊ C2
SylowC79 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC2×C42C22×D79
commutatorC2×C79C23×C42
FrattiniC2×C4C24×D79
FittingC2×C4×M16×C79C2
socleC23×C79C23×C4
prime radicalC24×D79C2×C4
cosocleC2×C4×C79C25
hypercenterC2×C4×M16D79
hypocenterC79C22×C4×M16
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1032952);