Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C71 · Schur multiplier (H2) = C22 |
| direct product | C71×#7288 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | #102 |
| commutator | C2×C8 | C42×C71 |
| Frattini, cosocle | C2×C4×C8 | C22×C71 |
| socle | C22×C71 | #340 |
| prime radical | C23×C71 | #107 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C2×C42×C71 ◁ C2×C4×C8×C71 ◁ G | |
202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 2 generators on 103 points:
(1,2,4,7,5,8,12,15)(3,9,11,16,10,6,13,14)(18,23)(19,27)(20,29)(21,28)(24,25)(26,32)(30,31)(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)(2,6,8,9)(4,11)(5,10)(7,14,15,16)(12,13)(17,18,20,24,21,25,19,23,22,26,27,31,28,30,29,32)4118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 276);