Finite Group Databasebeta

C2×#11926571 #14572194

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11926571

Splittings

SylowC19 ⋊ C2×#424

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC22×C19C23×C4
FrattiniC2×C4C23×D19
FittingC2×C19×#117C2
socleC23×C19C22×C4
prime radicalC24×C19C2×C4
cosocleC2×C4×C19C24
hypercenterC2×#117D19
hypocenterC19C2×#424
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×#117

512 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#18088539, #18088541, #18088546, …
maximal normal subgroup of#18088539, #18088541, #18088546, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 13069);