Finite Group Databasebeta

C2×#30630273 #44543086

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#30630273

Splittings

FittingC22×C8×C499 ⋊ C2
SylowC499 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23D1996
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
FittingC22×C8×C499C2
socleC23×C499D4
prime radicalC22×D1996C2
cosocleC2×C4×C499C23
hypercenterC22×C8D499
hypocenterC499C2×#102
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

7996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 537);