Finite Group Databasebeta

C4×#11926307 #18087720

order4864
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11926307

Splittings

SylowC19 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23×C4D76
commutatorC4×C19C43
FrattiniC23×C4C22×D19
FittingC22×C4×C8×C19C2
socle, prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC22×C4×C8D19
hypocenterC19C4×#340
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4864

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, 74749);