Finite Group Databasebeta

← Prev (#20269172) Next (#20269174) →

C22×C3×C5×C37⋊C3 #20269173

order6660
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C5×C37⋊C3

Splittings

Fitting, socleC22×C3×C5×C37 ⋊ C3
derived, SylowC37 ⋊ C22×C32×C5
HallC22×C5×C37 ⋊ C32
HallC5×C37 ⋊ C22×C32
HallC22×C37 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5C37⋊C3
commutator, hypocenterC37C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C37C3
LCSG ▷ C37
UCSC1 ◁ C22×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

900 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C3×C25×C37⋊C3, C2×C3×C5×D5×C37⋊C3, C22×C3×C52×C37⋊C3
maximal normal subgroup ofC22×C3×C25×C37⋊C3, C22×C3×C52×C37⋊C3
maximal quotient ofC22×C3×C25×C37⋊C3, C2×C3×C5×D5×C37⋊C3, C22×C3×C52×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 170);