Finite Group Databasebeta

C2×C22⋊(C499⋊C8) #44543059

order31936
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊(C499⋊C8)

Splittings

SylowC499 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D499
commutatorC2×C499C22×C8
FrattiniC2×C4C22×D499
FittingC23×C4×C499C2
socleC23×C499C2×C4
prime radicalC24×C499C4
cosocleC2×C4×C499C23
hypercenterC23×C4D499
hypocenterC499C2×C22⋊C8
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C22×C4 ◁ C23×C4

202 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, 510);