Finite Group Databasebeta

C2×#14561544 #18072901

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

Aliases

direct productC2×#14561544

Splittings

SylowC19 ⋊ C2×#1306

Subgroups

subgroupG/H
centerC23C19⋊#95
commutatorC23×C19C2×C42
FrattiniC23×C4C22×D19
FittingC2×C19×#407C2
socleC23×C19#95
prime radicalC25×C19C2×C4
cosocleC23×C4×C19C23
hypercenterC2×#407D19
hypocenterC19C2×#1306
LCSG ▷ C23×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59930);