Finite Group Databasebeta

C2×#14561537 #18072827

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

Aliases

direct productC2×#14561537

Splittings

SylowC19 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC22×C4(C2×D19)⋊C4
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC2×C19×#431C2
socleC23×C19#95
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#431D19
hypocenterC19C2×#1303
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

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, 59856);