Finite Group Databasebeta

C3×D7×D193 #30633889

order16212
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D7×D193

Splittings

Fitting, socle, HallC3×C7×C193 ⋊ C22
derived, HallC7×C193 ⋊ C22×C3
HallC3×C193 ⋊ C2×D7
SylowC193 ⋊ C2×C3×D7
HallC3×C7 ⋊ C2×D193
SylowC7 ⋊ C2×C3×D193

Subgroups

subgroupG/H
center, hypercenterC3D7×D193
commutator, cosocle, hypocenterC7×C193C22×C3
FrattiniC1G
Fitting, socleC3×C7×C193C22
LCSG ▷ C7×C193
UCSC1 ◁ C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4053

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16212, 52);