Finite Group Databasebeta

C42×C4⋊Dic79 #34209348

order20224
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC42×C4⋊Dic79

Splittings

SylowC79 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC22×C42C2×D79
commutatorC2×C79C2×C43
FrattiniC24C23×D79
FittingC2×C43×C79C2
socle, prime radical, cosocleC24×C79C24
hypercenterC2×C43D79
hypocenterC79C42×C4⋊C4
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C42 ◁ C2×C43

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20224

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, 90647);