Finite Group Databasebeta

C2×#41×Dic19 #14576817

order2432
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×Dic19

Splittings

SylowC19 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC22×C4C22×D19
commutatorC2×C19C24×C4
FrattiniC22C24×D19
Fitting, prime radicalC22×#41×C19C2
socleC23×C19C24
cosocleC22×C19C25
hypercenterC22×#41D19
hypocenterC19C2×C4×#41
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×#41

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18087946, #18087949, #18088001, …
maximal normal subgroup of#18087946, #18087949, #18088001, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17692);