Finite Group DatabasebetaFinite Group Databasebeta| order | 26574 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C43×C103 ⋊ C2×C3 |
| Hall | #27210791 ⋊ C2 |
| Hall | D4429 ⋊ C3 |
| Sylow | C103 ⋊ D43⋊C3 |
| 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)(40,78,73,58,59,57)(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)(105,109,110,106,107,111)(108,117,118,112,113,127)(114,130,131,120,121,139)(115,129,125,123,119,116)(122,135,137,126,128,140)(124,141,142,133,132,136)(134,144,145,143,138,146);(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)(104,105,108,114,122,125,110,109,115,124,134,142,118,129,117,128,138,145,131,140,141,130,121,132,137,139,146,144,135,113,119,127,136,143,133,123,107,111,116,126,120,112,106)Polycyclic presentation:
2,3,43,103|c^a=c^42,d^a=d^102,c^b=c^36,d^b=d^46744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26574, 24);