Finite Group Databasebeta

C4×C22⋊Dic499 #44542946

order31936
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C22⋊Dic499

Splittings

SylowC499 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D499
commutatorC2×C499C2×C42
FrattiniC23C22×D499
FittingC23×C4×C499C2
socle, cosocleC23×C499C23
prime radicalC24×C499C22
hypercenterC23×C4D499
hypocenterC499C4×C22⋊C4
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C22×C4 ◁ C23×C4

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

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, 397);