Finite Group Databasebeta

C2×#11927311 #14578345

order2432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#11927311

Splittings

SylowC19 ⋊ C2×#568

Subgroups

subgroupG/H
centerC2×C4C23×D19
commutatorC2×C19C24×C4
FrattiniC4C24×D19
Fitting, prime radicalC22×#41×C19C2
socleC22×C19C23×C4
cosocleC4×C19C25
hypercenterC22×#41D19
hypocenterC19C2×#568
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×#41

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18087866, #18087869, #18087876, …
maximal normal subgroup of#18087866, #18087869, #18087876, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19220);