Finite Group Databasebeta

#108×D499 #44543142

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

Aliases

direct product#108×D499

Splittings

Fitting#108×C499 ⋊ C2
SylowC499 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
Fitting#108×C499C2
socleC2×C499C2×C4⋊C4
prime radicalC22×D499Q8
cosocleC2×C4×C499C23
hypercenter#108D499
hypocenterC499C2×#108
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7984

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, 593);