Finite Group Databasebeta

C2×#30628276 #44537139

order31424
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30628276

Splittings

FittingC2×C16×C491 ⋊ C2
SylowC491 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D491
commutatorC2×C491C22×C8
FrattiniC8C22×D491
FittingC2×C16×C491C2
socleC22×C491C2×C8
prime radicalC22×D491C8
cosocleC8×C491C23
hypercenterC2×C16D491
hypocenterC491C2×M32
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

7880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 963);