Finite Group Databasebeta

C2×#11927344 #14578382

order2432
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#11927344

Splittings

FittingC22×M16×C19 ⋊ C2
SylowC19 ⋊ C2×#575

Subgroups

subgroupG/H
centerC2×C4C2×D76
commutator, cosocleC4×C19C25
FrattiniC4C24×D19
FittingC22×M16×C19C2
socleC22×C19C22×D4
hypercenterC22×M16D19
hypocenterC19C2×#575
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

1484 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#18089309, #18089313, #18089316, …
maximal normal subgroup of#18089309, #18089313, #18089316, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 19257);