Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D15225 |
| unambiguous semidirect product | C3⋊D5075 |
| unambiguous semidirect product | C7⋊D2175 |
| unambiguous semidirect product | C25⋊D609 |
| unambiguous semidirect product | C29⋊D525 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C25×C29 | C2 |
| Frattini | C5 | D3045 |
| socle | C3×C5×C7×C29 | D5 |
| LCS | G ▷ C3×C7×C25×C29 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 15225 |
A minimal faithful permutation representation — 2 generators on 64 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);(2,3)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(30,35)(31,34)(32,33)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)Polycyclic presentation:
2,3,5,7,29,5|c^5=f^4,b^a=b^2,c^a=c^4f,d^a=d^6,e^a=e^28,f^a=f^47614 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D15225 |
| maximal normal subgroup of | C2×D15225 |
| maximal quotient of | Dic15225, C2×D15225 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 18);