Finite Group Databasebeta

C2×#30630269 #44543077

order31936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30630269

Splittings

SylowC499 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22(C2×D499)⋊C4
commutatorC22×C499C22×C4
FrattiniC2×C4C22×D499
FittingC2×M16×C499C2
socleC22×C499C22⋊C4
prime radicalC23×C499C2×C4
cosocleC2×C4×C499C23
hypercenterC2×M16D499
hypocenterC499C2×#101
LCSG ▷ C22×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15968

Conjugacy classes & character table

5002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 528);