Finite Group Databasebeta

← Prev (#44525884) Next (#44525886) →

C5×D7×D221 #44525885

order30940
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D7×D221
unambiguous semidirect product(C13×D7)⋊(C5×D17)
unambiguous semidirect product(D7×C17)⋊(C5×D13)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C22
derived, HallC7×C13×C17 ⋊ C22×C5
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×C5×D13
HallC7×C13 ⋊ C2×C5×D17
HallC5×C17 ⋊ D7×D13
HallC5×C13 ⋊ D7×D17
HallC5×C7 ⋊ C2×D221
SylowC17 ⋊ C5×D7×D13
SylowC13 ⋊ C5×D7×D17
SylowC7 ⋊ C2×C5×D221

Subgroups

subgroupG/H
center, hypercenterC5D7×D221
commutator, cosocle, hypocenterC7×C13×C17C22×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C7×C13×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 7735

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 35);