Finite Group DatabasebetaFinite Group Databasebeta| order | 32980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8245 |
| derived, Hall | C5×C17×C97 ⋊ C4 |
| Hall | C17×C97 ⋊ Dic5 |
| Hall | C5×C97 ⋊ Dic17 |
| Sylow | C97 ⋊ Dic85 |
| Hall | C5×C17 ⋊ Dic97 |
| Sylow | C17 ⋊ Dic485 |
| Sylow | C5 ⋊ Dic1649 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8245 |
| commutator, hypocenter | C5×C17×C97 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C17×C97 | C2 |
| LCS | G ▷ C5×C17×C97 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 32980 |
A minimal faithful permutation representation — 2 generators on 123 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)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,3,2,4)(6,9)(7,8)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(28,123)(29,122)(30,121)(31,120)(32,119)(33,118)(34,117)(35,116)(36,115)(37,114)(38,113)(39,112)(40,111)(41,110)(42,109)(43,108)(44,107)(45,106)(46,105)(47,104)(48,103)(49,102)(50,101)(51,100)(52,99)(53,98)(54,97)(55,96)(56,95)(57,94)(58,93)(59,92)(60,91)(61,90)(62,89)(63,88)(64,87)(65,86)(66,85)(67,84)(68,83)(69,82)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76)Polycyclic presentation:
2,5,17,97,2|a^2=e,b^a=b^4,c^a=c^16,d^a=d^968248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32980, 8);