Finite Group Databasebeta

C2×#11926402 #14566006

order2432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#11926402

Splittings

SylowC19 ⋊ C2×#380

Subgroups

subgroupG/H
centerC24C22×D19
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC22×C22⋊C4×C19C2
socleC24×C19C23
prime radicalC25×C19C22
cosocleC23×C19C24
hypercenterC22×C22⋊C4D19
hypocenterC19C2×#380
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1232 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#18088372, #18088402, #18089461, …
maximal normal subgroup of#18088372, #18088402, #18089461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6881);