Finite Group Databasebeta

← Prev (#14576847) Next (#14576849) →

2−1+4×Dic19 #14576848

order2432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×Dic19

Splittings

SylowC19 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC22C24×D19
commutatorC2×C19C24×C4
Fitting, prime radicalC2×C19×2−1+4C2
socle, cosocleC22×C19C25
hypercenterC2×2−1+4D19
hypocenterC19C4×2−1+4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×2−1+4

1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17723);