Finite Group Databasebeta

C2×#11926506 #14572069

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11926506

Splittings

FittingC2×C19×C22⋊C8 ⋊ C2
SylowC19 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC22×C19C23×C4
FrattiniC2×C4C23×D19
FittingC2×C19×C22⋊C8C2
socleC23×C19C22×C4
prime radicalC24×D19C4
cosocleC2×C4×C19C24
hypercenterC2×C22⋊C8D19
hypocenterC19C2×#407
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18072137, #18072143, #18072149, …
maximal normal subgroup of#18072137, #18072143, #18072149, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 12944);