Finite Group Databasebeta

C2×#30630349 #44543640

order31936
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#30630349

Splittings

SylowC499 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
centerC23C22×D499
commutator, cosocleC22×C499C24
FrattiniC22C23×D499
FittingC22×Q8×C499C2
socle, prime radicalC23×C499C23
hypercenterC22×Q8D499
hypocenterC499C2×C4⋊Q8
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C23 ◁ C22×Q8

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

Conjugacy classes & character table

5008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 1091);