Finite Group Databasebeta

C2×#14561481 #18072186

order4864
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14561481

Splittings

SylowC19 ⋊ C2×#1282

Subgroups

subgroupG/H
centerC22×C4(C2×D19)⋊C4
commutatorC22×C19C2×C4×C8
FrattiniC23×C4C22×D19
FittingC22×C19×C22⋊C8C2
socleC23×C19#95
prime radicalC25×C19C2×C4
cosocleC23×C4×C19C23
hypercenterC22×C22⋊C8D19
hypocenterC19C2×#1282
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59215);