Finite Group Databasebeta

C2×#14561468 #18071975

order4864
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#14561468

Splittings

SylowC19 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC2×C42D76
commutatorC4×C19C2×C4×C8
FrattiniC2×C42C22×D19
FittingC2×C43×C19C2
socleC23×C19#95
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×C43D19
hypocenterC19C2×#1276
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C43

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59004);