Finite Group Databasebeta

C2×#11926443 #14566087

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

Aliases

direct productC2×#11926443

Splittings

SylowC19 ⋊ C2×#389

Subgroups

subgroupG/H
centerC24C22×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC22×C4⋊C4×C19C2
socle, prime radicalC24×C19C23
cosocleC23×C19C24
hypercenterC22×C4⋊C4D19
hypocenterC19C2×#389
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C4⋊C4

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18088528, #18088533, #18088552, …
maximal normal subgroup of#18088528, #18088533, #18088552, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6962);