Finite Group Databasebeta

C2×#11926319 #14565224

order2432
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#11926319

Splittings

SylowC19 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D19
commutatorC2×C19C2×C4×C8
FrattiniC2×C8C22×D19
FittingC22×C16×C19C2
socle, prime radicalC23×C19C2×C8
cosocleC2×C8×C19C23
hypercenterC22×C16D19
hypocenterC19C2×#346
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C8 ◁ C22×C16

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18070227, #18070231
maximal normal subgroup of#18070227, #18070231

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6099);