Finite Group DatabasebetaFinite Group Databasebeta| order | 26058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C101⋊(D43⋊C3) |
| unambiguous semidirect product | (C43⋊C3)⋊D101 |
| unambiguous semidirect product | D4343⋊C3 |
| Fitting, socle, derived, Hall | C43×C101 ⋊ C2×C3 |
| Hall | C101×C43⋊C3 ⋊ C2 |
| Hall | D4343 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D101 |
| Sylow | C101 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C3×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C101 | C2×C3 |
| LCS | G ▷ C43×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 144 |
| transitive degree | μt(G) = 4343 |
A minimal faithful permutation representation — 2 generators on 144 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)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(103,107,108,104,105,109)(106,115,116,110,111,125)(112,128,129,118,119,137)(113,127,123,121,117,114)(120,133,135,124,126,138)(122,139,140,131,130,134)(132,142,143,141,136,144);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,103,106,112,120,123,108,107,113,122,132,140,116,127,115,126,136,143,129,138,139,128,119,130,135,137,144,142,133,111,117,125,134,141,131,121,105,109,114,124,118,110,104)Polycyclic presentation:
2,3,43,101|c^a=c^42,d^a=d^100,c^b=c^36863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26058, 12);