Finite Group Databasebeta

← Prev (#27189189) Next (#27189191) →

C2×C5×C7×D31⋊C3 #27189190

order13020
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D31⋊C3
unambiguous semidirect product(C2×C5×D31)⋊(C3×C7)

Splittings

Fitting, socleC2×C5×C7×C31 ⋊ C2×C3
derived, SylowC31 ⋊ C22×C3×C5×C7
HallC2×C5×C7×D31 ⋊ C3
HallC5×C7×C31⋊C3 ⋊ C22
HallC5×C7×C31 ⋊ C22×C3
HallC2×C7×D31 ⋊ C3×C5
HallC7×C31⋊C3 ⋊ C22×C5
HallC2×C5×D31 ⋊ C3×C7
HallC5×C31⋊C3 ⋊ C22×C7
HallC7×C31 ⋊ C22×C3×C5
HallC5×C31 ⋊ C22×C3×C7
HallC2×D31 ⋊ C3×C5×C7
HallC31⋊C3 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D31⋊C3
commutator, cosocle, hypocenterC31C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 2170

A minimal faithful permutation representation — 2 generators on 45 points:

(2,6,7,3,4,8)(5,14,15,9,10,22)(11,24,25,17,18,30)(12,23,19,20,16,13)(21,31,28,27,26,29)(32,33,34,35,36,37,38)(39,40,41,42,43);(1,2,5,11,19,7,6,12,21,28,15,23,14,18,26,25,30,31,24,10,16,22,29,27,20,4,8,13,17,9,3)(44,45)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 157);