Finite Group Databasebeta

C2×C4×D4×D19 #14576802

order2432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4×D4×D19

Splittings

FittingC2×C4×D4×C19 ⋊ C2
SylowC19 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC2×C19C24×C4
FrattiniC22C24×D19
FittingC2×C4×D4×C19C2
socleC23×C19C24
prime radicalC22×D4×D19C2
cosocleC22×C19C25
hypercenterC2×C4×D4D19
hypocenterC19C22×C4×D4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 608

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18073904
maximal normal subgroup of#18073904

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17677);