Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C27 |
| direct product | C71×#23898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C22×C4×C71 ◁ G | |
1718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,7)(4,14)(5,17)(6,10)(8,16)(9,19)(11,26)(12,29)(13,22)(15,25)(18,24)(20,28)(21,31)(23,30)(27,32)(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);(1,3,6,13)(2,7,10,22)(4,11,15,27)(5,12,19,31)(8,23,24,20)(9,21,17,29)(14,32,25,26)(16,28,18,30);(1,4)(2,8)(3,11)(5,18)(6,15)(7,20)(9,25)(10,24)(12,30)(13,27)(14,17)(16,19)(21,32)(22,23)(26,29)(28,31);(5,19)(9,17)(12,31)(14,25)(16,18)(21,29)(26,32)(28,30)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16886);