Finite Group Databasebeta

← Prev (#26042885) Next (#26042887) →

C3×C5×C7×C37⋊C3 #26042886

order11655
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C7×C37⋊C3
unambiguous semidirect productC37⋊(C32×C5×C7)
unambiguous semidirect product(C3×C37)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C37)⋊(C32×C7)
unambiguous semidirect product(C3×C5×C37)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C3
derived, SylowC37 ⋊ C32×C5×C7
HallC5×C7×C37 ⋊ C32
HallC7×C37 ⋊ C32×C5
HallC5×C37 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C37⋊C3
commutator, cosocle, hypocenterC37C32×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C37C3
LCSG ▷ C37
UCSC1 ◁ C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1575 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C7×D37⋊C3, C3×C5×(C37⋊C3)⋊D7, C3×C5×D7×C37⋊C3, …
maximal normal subgroup ofC3×C5×C7×D37⋊C3, C3×C5×(C37⋊C3)⋊D7, C3×C5×D7×C37⋊C3, …
maximal quotient ofC2×C3×C5×C7×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11655, 14);