Finite Group Databasebeta

C2×#11926348 #14565337

order2432
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#11926348

Splittings

SylowC19 ⋊ C2×#358

Subgroups

subgroupG/H
centerC23#64525
commutatorC8×C19C22×C4
FrattiniC2×C8C22×D19
FittingC22×Q16×C19C2
socle, prime radicalC23×C19D8
cosocleC2×C8×C19C23
hypercenterC22×Q16D19
hypocenterC19C2×#358
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

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

normal subgroups only

This group has 232 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) = 2432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6212);