Finite Group Databasebeta

C2×C19×C4⋊Dic3 #14269677

order1824
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23

Aliases

direct productC2×C19×C4⋊Dic3

Splittings

HallC3×C19 ⋊ C2×C4⋊C4
SylowC3 ⋊ C2×C4⋊C4×C19

Subgroups

subgroupG/H
centerC23×C19C2×D3
commutatorC2×C3C22×C4×C19
FrattiniC22C22×D3×C19
FittingC22×C3×C4×C19C2
socle, prime radicalC23×C3×C19C22
cosocleC22×C3C23×C19
hypercenterC22×C4×C19D3
hypocenterC3C2×C4⋊C4×C19
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C19 ◁ C22×C4×C19

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1824

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 904);