Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C71 · Schur multiplier (H2) = C28 |
| direct product | C71×#61636 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C71 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ #525×C71 ◁ G | |
2074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 5 generators on 111 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,16)(12,23)(13,18)(14,27)(15,19)(17,24)(20,35)(21,30)(22,31)(25,33)(26,32)(28,34)(29,38)(36,39)(37,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,3)(2,5)(4,8)(6,7)(9,11,15,22)(10,16,19,31)(12,20,25,37)(13,26,14,21)(17,29,34,39)(18,32,27,30)(23,35,33,40)(24,38,28,36);(9,12)(10,17)(11,20)(13,24)(14,28)(15,25)(16,29)(18,33)(19,34)(21,36)(22,37)(23,27)(26,38)(30,35)(31,39)(32,40);(3,8)(5,7)(9,13,15,14)(10,18,19,27)(11,21,22,26)(12,24,25,28)(16,30,31,32)(17,33,34,23)(20,36,37,38)(29,35,39,40);(2,6)(5,7)(11,22)(16,31)(20,37)(21,26)(29,39)(30,32)(35,40)(36,38)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 54624);