Finite Group Databasebeta

C4×#11926283 #18073454

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11926283

Splittings

FittingC4×C19×#97 ⋊ C2
SylowC19 ⋊ C4×#329

Subgroups

subgroupG/H
centerC22×C4(C2×D19)⋊C4
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC4×C19×#97C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenterC4×#97D19
hypocenterC19C4×#329
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

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, 60483);