Finite Group DatabasebetaFinite Group Databasebeta| order | 488 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C61 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #6923 |
| commutator, hypocenter | C61 | C8 |
| Fitting, socle, prime radical | C2×C61 | C4 |
| cosocle | Dic61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 488 |
A minimal faithful permutation representation — 2 generators on 69 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,49)(36,51,52,60)(40,55,56,58)(44,59,57,54)(46,61,53,50)(62,63,64,66,65,67,68,69);(1,2,5,10,19,32,49,61,42,25,12,3,7,14,23,36,53,45,60,59,38,21,8,16,27,40,57,43,28,41,58,55,34,17,29,44,56,39,26,15,24,37,54,51,30,46,52,35,22,13,6,11,20,33,50,47,48,31,18,9,4)Polycyclic presentation:
2^3,61|a^2=b,b^2=c,d^a=d^11,d^b=d^6038 conjugacy classes — view the full character table.
| maximal subgroup of | D61⋊C8, #11758213, C2×#92420, … |
| maximal normal subgroup of | D61⋊C8, #11758213, C2×#92420, … |
| maximal quotient of | #11758187, C2×#92420, C3×#92420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(488, 3);