Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C71 · Schur multiplier (H2) = C22×C4 |
| direct product | C71×#7894 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C2×D4 |
| commutator | C2×C4 | C2×C42×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| socle | C23×C71 | C2×C22⋊C4 |
| prime radical | C24×C71 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ C22×C42×C71 ◁ G | |
614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2)(3,4)(5,6)(7,15)(8,12)(9,13)(10,14)(11,16)(17,20)(18,19)(21,22,25,29,26,30,24,28)(23,31,32,35,34,36,33,27)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,4)(5,7,9,17,10,18,8,16)(6,11,12,19,14,20,13,15)(21,23)(22,27,30,35)(24,33)(25,32)(26,34)(28,36,29,31);(5,8,10,9)(6,12,14,13)(7,16,18,17)(11,19,20,15)(21,24,26,25)(22,28,30,29)(23,32,34,33)(27,31,35,36)5396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 882);