Finite Group Databasebeta

#106×D499 #44543127

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#106×D499

Splittings

Fitting#106×C499 ⋊ C2
SylowC499 ⋊ C2×#106

Subgroups

subgroupG/H
centerC22D4×D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
Fitting#106×C499C2
socleC22×C499C2×D4
prime radicalC22×D499D4
cosocleC2×C4×C499C23
hypercenter#106D499
hypocenterC499C2×#106
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

3514 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 578);