Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#19515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | #532×C71 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,5,9)(3,6,10,14)(4,7,12,8)(11,13,16,15)(18,22)(19,26)(20,23)(25,30)(27,28)(29,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3)(2,6)(4,11)(5,10)(7,13)(8,15)(9,14)(12,16)(17,18,23,30,21,25,20,22)(19,24,26,31,27,32,28,29);(2,7)(4,12)(6,13)(8,9)(11,16)(14,15)(17,19)(18,24)(20,28)(21,27)(22,29)(23,26)(25,32)(30,31);(3,10)(6,14)(11,16)(13,15)(18,25)(19,27)(22,30)(26,28)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12503);