Finite Group DatabasebetaFinite Group Databasebeta| order | 32844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8211 |
| unambiguous semidirect product | C3⋊Dic2737 |
| unambiguous semidirect product | C7⋊Dic1173 |
| unambiguous semidirect product | C23⋊Dic357 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8211 |
| commutator, hypocenter | C3×C7×C17×C23 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C17×C23 | C2 |
| LCS | G ▷ C3×C7×C17×C23 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 32844 |
A minimal faithful permutation representation — 2 generators on 54 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);(1,3,2,4)(6,7)(9,14)(10,13)(11,12)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)Polycyclic presentation:
2,3,7,17,23,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^16,e^a=e^228214 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32844, 17);