Finite Group Databasebeta

← Prev (#44501657) Next (#44501659) →

C5×D3069 #44501658

order30690
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3069
unambiguous semidirect productC9⋊(C5×D341)

Splittings

Fitting, HallC5×C9×C11×C31 ⋊ C2
derived, HallC9×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ D9
HallC5×C9×C31 ⋊ D11
HallC5×C9×C11 ⋊ D31
HallC11×C31 ⋊ C5×D9
HallC9×C31 ⋊ C5×D11
HallC5×C31 ⋊ D99
HallC9×C11 ⋊ C5×D31
HallC5×C11 ⋊ D279
HallC5×C9 ⋊ D341
SylowC31 ⋊ C5×D99
SylowC11 ⋊ C5×D279
SylowC9 ⋊ C5×D341

Subgroups

subgroupG/H
center, hypercenterC5D3069
commutator, cosocle, hypocenterC9×C11×C31C2×C5
FrattiniC3C5×D1023
FittingC5×C9×C11×C31C2
socleC3×C5×C11×C31D3
LCSG ▷ C9×C11×C31
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 15345

A minimal faithful permutation representation — 2 generators on 56 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56);(7,14)(8,13)(9,12)(10,11)(16,25)(17,24)(18,23)(19,22)(20,21)(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

7680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 25);