Finite Group DatabasebetaFinite Group Databasebeta| order | 34602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C79⋊C3)⋊D73 |
| Fitting, socle, derived, Hall | C73×C79 ⋊ C2×C3 |
| Hall | C73×C79⋊C3 ⋊ C2 |
| Hall | D5767 ⋊ C3 |
| Hall | C79⋊C3 ⋊ D73 |
| Sylow | C79 ⋊ C3×D73 |
| Sylow | C73 ⋊ D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73×C79 | C2×C3 |
| LCS | G ▷ C73×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 152 |
| transitive degree | μt(G) = 5767 |
A minimal faithful permutation representation — 2 generators on 152 points:
(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)(64,65)(66,67)(68,69)(70,71)(72,73)(75,79,80,76,77,81)(78,87,88,82,83,97)(84,100,101,90,91,114)(85,99,95,93,89,86)(92,119,120,103,104,136)(94,117,118,106,102,111)(96,98,116,108,109,112)(105,140,141,122,123,151)(107,139,124,125,121,133)(110,115,138,127,128,134)(113,147,146,131,132,130)(126,152,144,143,142,149)(129,137,148,145,135,150);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(74,75,78,84,92,105,124,101,116,117,100,115,135,104,121,132,134,136,149,143,125,106,93,77,81,86,96,110,129,146,118,88,99,87,98,113,123,142,141,148,150,151,152,140,131,109,83,89,97,111,130,145,127,108,95,80,79,85,94,107,126,144,120,138,147,139,119,137,128,91,102,112,114,133,122,103,90,82,76)Polycyclic presentation:
2,3,73,79|c^a=c^72,d^a=d^78,d^b=d^231063 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34602, 21);