Finite Group Databasebeta

#101×D499 #44543076

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

Aliases

direct product#101×D499

Splittings

Fitting#101×C499 ⋊ C2
SylowC499 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D499
commutatorC22×C499C22×C4
FrattiniC2×C4C22×D499
Fitting#101×C499C2
socleC2×C499C2×C22⋊C4
prime radicalC22×D499C2×C4
cosocleC2×C4×C499C23
hypercenter#101D499
hypocenterC499C2×#101
LCSG ▷ C22×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7984

Conjugacy classes & character table

2761 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 527);