Finite Group Databasebeta

C4×#11926279 #18073416

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11926279

Splittings

FittingC4×C19×C22⋊C8 ⋊ C2
SylowC19 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22×C4(C2×D19)⋊C4
commutatorC2×C4×C19C2×C42
FrattiniC23×C4C22×D19
FittingC4×C19×C22⋊C8C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenterC4×C22⋊C8D19
hypocenterC19C4×#327
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

816 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, 60445);