Finite Group Databasebeta

C2×#11926370 #14565412

order2432
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#11926370

Splittings

SylowC19 ⋊ C2×#366

Subgroups

subgroupG/H
centerC23D152
commutatorC8×C19C22×C4
FrattiniC2×C8C22×D19
FittingC22×C16×C19C2
socle, prime radicalC23×C19D8
cosocleC2×C8×C19C23
hypercenterC22×C16D19
hypocenterC19C2×#366
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18070239, #18070240, #18070257, …
maximal normal subgroup of#18070239, #18070240, #18070257, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6287);