Finite Group DatabasebetaFinite Group Databasebeta| order | 24102 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22548781 |
| Fitting, socle, derived | C3×C13×C103 ⋊ C2×C3 |
| Hall | C3×#16860815 ⋊ C2 |
| Hall | C13×C103 ⋊ C3×D3 |
| Sylow | C103 ⋊ D3×C13⋊C3 |
| Sylow | C13 ⋊ C3⋊(D103⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C103 | C2×C3 |
| LCS | G ▷ C3×C13×C103 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 4017 |
A minimal faithful permutation representation — 2 generators on 119 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,88)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,78,73,58,59,57)(51,83,84,72,63,98)(53,90,91,74,71,86)(56,65,89,76,77,87)(60,94,93,79,80,82)(75,99,100,92,85,102)(81,103,97,95,96,101)(105,106,108)(107,110,113)(109,112,111)(114,116,115)(118,119);(1,2,5,11,19,32,51,73,45,15,26,14,25,40,60,81,97,91,47,66,78,67,46,65,50,71,80,84,87,88,102,103,99,83,55,18,29,39,41,61,82,92,74,52,33,20,4,8,13,23,37,56,76,54,35,22,7,6,12,21,34,53,75,93,68,28,43,44,27,42,63,85,96,100,70,89,98,94,90,69,77,31,48,59,62,64,86,101,95,79,58,36,10,16,24,38,57,72,49,30,17,9,3)(104,105,107,106,109,113,110,114,116,108,111,115,112)(117,118,119)Polycyclic presentation:
2,3^2,13,103|c^a=c^2,e^a=e^102,d^b=d^3,e^b=e^46684 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24102, 51);