Finite Group Databasebeta

C4×#11926312 #18087744

order4864
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#11926312

Splittings

SylowC19 ⋊ C4×#343

Subgroups

subgroupG/H
centerC22×C4(C2×D19)⋊C4
commutatorC22×C19C43
FrattiniC23×C4C22×D19
FittingC2×C4×M16×C19C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22×C4
cosocleC23×C4×C19C23
hypercenterC2×C4×M16D19
hypocenterC19C4×#343
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

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, 74773);