Finite Group Databasebeta

C2×#14561511 #18072502

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14561511

Splittings

SylowC19 ⋊ C2×#1293

Subgroups

subgroupG/H
centerC23C19⋊#95
commutatorC2×C4×C19C2×C42
FrattiniC23×C4C22×D19
FittingC2×C19×#407C2
socleC23×C19#95
prime radicalC25×C19Q8
cosocleC23×C4×C19C23
hypercenterC2×#407D19
hypocenterC19C2×#1293
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59531);