Finite Group Databasebeta

C2×#11926651 #14572422

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11926651

Splittings

SylowC19 ⋊ C2×#441

Subgroups

subgroupG/H
centerC23D4×D19
commutatorC4×C19C23×C4
FrattiniC2×C4C23×D19
FittingC22×Q16×C19C2
socle, prime radicalC23×C19C2×D4
cosocleC2×C4×C19C24
hypercenterC22×Q16D19
hypocenterC19C2×#441
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

480 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 237 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, 13297);