Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#24410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C22×C4×C71 ◁ G | |
1322 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)(3,11,14,7)(4,16,17,8)(5,10)(6,9)(12,19,23,15)(13,22)(18,29,30,24)(20,21)(25,28)(26,31)(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);(1,3,6,14)(2,7,9,11)(4,13,17,28)(5,19,21,15)(8,22,16,25)(10,12,20,23)(18,31,30,27)(24,26,29,32);(1,2)(3,12)(4,8)(5,20)(6,9)(7,19)(10,21)(11,15)(13,26)(14,23)(16,17)(18,29)(22,31)(24,30)(25,27)(28,32);(1,4)(2,8)(3,13)(5,18)(6,17)(7,22)(9,16)(10,24)(11,25)(12,26)(14,28)(15,27)(19,31)(20,29)(21,30)(23,32)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 17398);