Finite Group DatabasebetaFinite Group Databasebeta| order | 24522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C61×C67 ⋊ C2×C3 |
| Hall | #27133912 ⋊ C2 |
| Hall | D4087 ⋊ C3 |
| Sylow | C67 ⋊ D61⋊C3 |
| Sylow | C61 ⋊ D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C67 | C2×C3 |
| LCS | G ▷ C61×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 4087 |
A minimal faithful permutation representation — 2 generators on 128 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)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,54,55,49,40,64)(34,61,62,50,48,57)(37,42,60,52,53,58)(51,65,66,63,56,67)(69,73,74,70,71,75)(72,81,82,76,77,91)(78,94,95,84,85,107)(79,93,89,87,83,80)(86,112,113,97,98,123)(88,110,111,99,96,104)(90,92,109,101,102,105)(100,125,126,115,114,121)(103,108,124,117,116,122)(106,128,127,119,120,118);(1,2,5,11,19,32,45,15,26,14,25,40,56,66,47,60,64,61,46,53,18,29,39,41,57,63,50,33,20,4,8,13,23,37,52,35,22,7,6,12,21,34,51,62,28,43,44,27,42,31,48,55,58,59,67,65,54,36,10,16,24,38,49,30,17,9,3)(68,69,72,78,86,98,114,120,122,123,117,101,89,74,73,79,88,100,116,85,96,105,107,121,127,111,82,93,81,92,106,119,102,77,83,91,104,118,126,95,109,110,94,108,115,99,87,71,75,80,90,103,113,124,128,125,112,97,84,76,70)Polycyclic presentation:
2,3,61,67|c^a=c^60,d^a=d^66,c^b=c^47,d^b=d^29687 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24522, 24);