Finite Group Databasebeta

C2×#30630261 #44543046

order31936
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30630261

Splittings

SylowC499 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D499
commutatorC2×C499C2×C42
FrattiniC2×C4C22×D499
FittingC22×C8×C499C2
socle, prime radicalC23×C499C2×C4
cosocleC2×C4×C499C23
hypercenterC22×C8D499
hypocenterC499C2×#97
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C22×C4 ◁ C22×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 497);