Finite Group Databasebeta

C2×#11927165 #14577013

order2432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#11927165

Splittings

FittingC2×C19×#117 ⋊ C2
SylowC19 ⋊ C2×#542

Subgroups

subgroupG/H
centerC23C23×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC2×C19×#117C2
socleC23×C19C24
prime radicalC2×#10597376C2
hypercenterC2×#117D19
hypocenterC19C2×#542
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#117

1132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18073968, #18073971, #18075044, …
maximal normal subgroup of#18073968, #18073971, #18075044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17888);