Finite Group Databasebeta

C2×#11926517 #14572091

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

Aliases

direct productC2×#11926517

Splittings

FittingC2×C19×#117 ⋊ C2
SylowC19 ⋊ C2×#410

Subgroups

subgroupG/H
centerC2×C4(C2×D19)⋊C4
commutatorC22×C19C23×C4
FrattiniC23C23×D19
FittingC2×C19×#117C2
socleC22×C19C2×C22⋊C4
prime radicalC22×#64541C2
cosocleC23×C19C24
hypercenterC2×#117D19
hypocenterC19C2×#410
LCSG ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18087865, #18087868, #18087870, …
maximal normal subgroup of#18087865, #18087868, #18087870, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 12966);