Finite Group Databasebeta

Q16×Dic499 #44543193

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

Aliases

direct productQ16×Dic499

Splittings

SylowC499 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC22D4×D499
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
FittingC2×Q16×C499C2
socle, prime radicalC22×C499C2×D4
cosocleC2×C4×C499C23
hypercenterC2×Q16D499
hypocenterC499C4×Q16
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

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, 644);