Finite Group Databasebeta

C2×C4×C22⋊Dic19 #14565965

order2432
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×C22⋊Dic19

Splittings

SylowC19 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D19
commutatorC2×C19C22×C42
FrattiniC23C23×D19
FittingC24×C4×C19C2
socleC24×C19C23
prime radicalC25×C19C22
cosocleC23×C19C24
hypercenterC24×C4D19
hypocenterC19C2×C4×C22⋊C4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C23×C4 ◁ C24×C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18072132, #18072144, C2×#14561481, …
maximal normal subgroup of#18072132, #18072144, C2×#14561481, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 6840);