Finite Group Databasebeta

C2×#11926308 #14563358

order2432
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#11926308

Splittings

SylowC19 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D19
commutatorC4×C19C2×C42
FrattiniC22×C4C22×D19
FittingC22×M16×C19C2
socleC23×C19C4⋊C4
prime radicalC24×C19Q8
cosocleC22×C4×C19C23
hypercenterC22×M16D19
hypocenterC19C2×#341
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#341×Dic19, C4×#11926308, #18087727, …
maximal normal subgroup of#341×Dic19, C4×#11926308, #18087727, …
maximal quotient ofC2×#14561469, #18071997, #18072004, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 4233);