Finite Group Databasebeta

C2×#11926321 #14565236

order2432
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11926321

Splittings

SylowC19 ⋊ C2×#347

Subgroups

subgroupG/H
centerC2×C4C4×Dic19
commutatorC4×C19C2×C42
FrattiniC2×C8C22×D19
FittingC2×C19×M32C2
socleC22×C19#97
prime radicalC23×C19M16
cosocleC2×C8×C19C23
hypercenterC2×M32D19
hypocenterC19C2×#347
LCSG ▷ C4×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×M32

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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) = 608

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6111);