Finite Group Databasebeta

C4×Dic499⋊C4 #44542951

order31936
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×Dic499⋊C4

Splittings

SylowC499 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D499
commutatorC2×C499C2×C42
FrattiniC23C22×D499
FittingC2×C42×C499C2
socle, prime radical, cosocleC23×C499C23
hypercenterC2×C42D499
hypocenterC499C4×C4⋊C4
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 402);