Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic5775 |
| unambiguous semidirect product | C3⋊Dic1925 |
| unambiguous semidirect product | C7⋊Dic825 |
| unambiguous semidirect product | C11⋊Dic525 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5775 |
| commutator, hypocenter | C3×C7×C11×C25 | C4 |
| Frattini | C2×C5 | D1155 |
| Fitting, cosocle | C2×C3×C7×C11×C25 | C2 |
| socle, prime radical | C2×C3×C5×C7×C11 | D5 |
| LCS | G ▷ C3×C7×C11×C25 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 23100 |
A minimal faithful permutation representation — 2 generators on 50 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);(1,3,2,4)(6,7)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(34,39)(35,38)(36,37)(41,50)(42,49)(43,48)(44,47)(45,46)Polycyclic presentation:
2,3,5,7,11,2,5|a^2=f,c^5=g^4,b^a=b^2,c^a=c^4g,d^a=d^6,e^a=e^10,g^a=g^45778 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic11550 |
| maximal normal subgroup of | Dic11550 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 19);