Finite Group DatabasebetaFinite Group Databasebeta| order | 26574 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C103⋊C3)⋊D43 |
| Fitting, socle, derived, Hall | C43×C103 ⋊ C2×C3 |
| Hall | C43×C103⋊C3 ⋊ C2 |
| Hall | D4429 ⋊ C3 |
| Hall | C103⋊C3 ⋊ D43 |
| Sylow | C103 ⋊ C3×D43 |
| Sylow | C43 ⋊ D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C103 | C2×C3 |
| LCS | G ▷ C43×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 146 |
| transitive degree | μt(G) = 4429 |
A minimal faithful permutation representation — 2 generators on 146 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)(40,79,77,58,59,57)(51,80,81,60,72,96)(53,91,92,73,71,85)(56,65,90,74,75,86)(63,98,94,82,83,78)(76,89,97,84,93,102)(87,103,101,99,100,95)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146);(1,2,5,11,19,32,51,58,36,10,16,24,38,57,78,95,99,75,31,48,59,62,64,85,70,90,98,72,91,69,89,100,102,96,68,28,43,44,27,42,63,84,74,54,35,22,7,6,12,21,34,53,73,52,33,20,4,8,13,23,37,56,76,82,55,18,29,39,41,61,81,97,103,93,50,71,80,83,86,88,92,47,66,79,67,46,65,87,101,94,77,45,15,26,14,25,40,60,49,30,17,9,3)(104,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,146,144,142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,112,110,108,106)Polycyclic presentation:
2,3,43,103|c^a=c^42,d^a=d^102,d^b=d^56800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26574, 21);