Finite Group Databasebeta

#41×Dic499 #44543569

order31936
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic499

Splittings

SylowC499 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D499
commutatorC2×C499C23×C4
FrattiniC22C23×D499
Fitting, prime radicalC2×#41×C499C2
socle, cosocleC22×C499C24
hypercenterC2×#41D499
hypocenterC499C4×#41
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

5020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 1020);