Finite Group DatabasebetaFinite Group Databasebeta| order | 60996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic15249 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D15249 |
| commutator, hypocenter | C3×C13×C17×C23 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C13×C17×C23 | C2 |
| LCS | G ▷ C3×C13×C17×C23 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 60996 |
A minimal faithful permutation representation — 2 generators on 60 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)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60);(1,3,2,4)(6,7)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)Polycyclic presentation:
2^2,3,13,17,23|a^2=b,c^a=c^2,d^a=d^12,e^a=e^16,f^a=f^2215252 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f");;
gap> coll := SingleCollector(F, [2, 2, 3, 13, 17, 23]);;
gap> SetPower(coll, 1, F.2);;
gap> SetConjugate(coll, 3, 1, F.3^2);;
gap> SetConjugate(coll, 4, 1, F.4^12);;
gap> SetConjugate(coll, 5, 1, F.5^16);;
gap> SetConjugate(coll, 6, 1, F.6^22);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);