Finite Group Databasebeta

C2×#11926526 #14572108

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

Aliases

direct productC2×#11926526

Splittings

FittingC22×M16×C19 ⋊ C2
SylowC19 ⋊ C2×#413

Subgroups

subgroupG/H
centerC2×C4(C2×D19)⋊C4
commutatorC22×C19C23×C4
FrattiniC2×C4C23×D19
FittingC22×M16×C19C2
socleC22×C19C2×C22⋊C4
prime radicalC22×#64541C2
cosocleC2×C4×C19C24
hypercenterC22×M16D19
hypocenterC19C2×#413
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18087875, #18087878, #18087885, …
maximal normal subgroup of#18087875, #18087878, #18087885, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 12983);