Finite Group Databasebeta

C2×#11926381 #14565935

order2432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11926381

Splittings

FittingC2×C19×Q32 ⋊ C2
SylowC19 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#10597283
commutator, cosocleC16×C19C23
FrattiniC16C22×D19
FittingC2×C19×Q32C2
socleC22×C19D16
prime radicalC2×D304C2
hypercenterC2×Q32D19
hypocenterC19C2×SD64
LCSG ▷ C16×C19 ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6810);