Finite Group Databasebeta

C2×#14561460 #18070481

order4864
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14561460

Splittings

SylowC19 ⋊ C2×#1272

Subgroups

subgroupG/H
centerC24(C2×D19)⋊C4
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC2×C19×#336C2
socle, prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#336D19
hypocenterC19C2×#1272
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4864

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 57510);