Finite Group Databasebeta

C2×#11926463 #14566844

order2432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11926463

Splittings

SylowC19 ⋊ C2×#395

Subgroups

subgroupG/H
centerC24C22×D19
commutator, cosocleC23×C19C24
FrattiniC23C23×D19
FittingC23×Q8×C19C2
socle, prime radicalC24×C19C23
hypercenterC23×Q8D19
hypocenterC19C2×#395
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×Q8

908 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 285 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) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18077530, #18077535, #18082753, …
maximal normal subgroup of#18077530, #18077535, #18082753, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 7719);