Finite Group Databasebeta

← Prev (#37552074) Next (#37552076) →

C3×C7×C5⋊(D37⋊C3) #37552075

order23310
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×C5⋊(D37⋊C3)
unambiguous semidirect productC5⋊(C3×C7×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(C3×C7×D5)
unambiguous semidirect productD185⋊(C32×C7)
unambiguous semidirect product(C3×D185)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C2×C32×C7
HallC3×C5×C7×C37⋊C3 ⋊ C2
HallC7×D185 ⋊ C32
HallC3×C7×C37⋊C3 ⋊ D5
HallC3×C5×C37⋊C3 ⋊ C2×C7
HallC5×C7×C37 ⋊ C2×C32
HallD185 ⋊ C32×C7
HallC3×C37⋊C3 ⋊ C7×D5
HallC7×C37 ⋊ C32×D5
SylowC37 ⋊ C32×C7×D5
HallC5×C7 ⋊ C3×D37⋊C3
SylowC5 ⋊ C3×C7×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C7C5⋊(D37⋊C3)
commutator, cosocle, hypocenterC5×C37C2×C32×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C3×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 94);