Finite Group Databasebeta

C2×#30630287 #44543144

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

Aliases

direct productC2×#30630287

Splittings

SylowC499 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1996
commutatorC4×C499C22×C4
FrattiniC2×C4C22×D499
FittingC22×C8×C499C2
socleC22×C499C4⋊C4
prime radicalC23×C499Q8
cosocleC2×C4×C499C23
hypercenterC22×C8D499
hypocenterC499C2×#108
LCSG ▷ C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 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, 595);