Finite Group Databasebeta

C2×#30628278 #44537145

order31424
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30628278

Splittings

FittingC2×D8×C491 ⋊ C2
SylowC491 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22#21463313
commutator, cosocleC8×C491C23
FrattiniC8C22×D491
FittingC2×D8×C491C2
socleC22×C491D8
hypercenterC2×D8D491
hypocenterC491C2×D16
LCSG ▷ C8×C491 ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

3452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 969);