Finite Group Databasebeta

C2×#30630270 #44543078

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

Aliases

direct productC2×#30630270

Splittings

SylowC499 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic499
commutatorC22×C499C22×C4
FrattiniC2×C4C22×D499
FittingC22×Q8×C499C2
socleC22×C499C22⋊C4
prime radicalC23×C499C2×C4
cosocleC2×C4×C499C23
hypercenterC22×Q8D499
hypocenterC499C2×#101
LCSG ▷ C22×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

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, 529);