Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C27 |
| direct product | C71×#23891 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C22×C4×C71 ◁ G | |
1622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,4)(5,6,10,15)(7,16,20,17)(8,22,24,30)(9,25,11,14)(12,21,28,19)(13,26,29,23)(18,27,34,36)(31,35,32,33)(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);(5,7,10,20)(6,12,15,28)(8,18,24,34)(9,21,11,19)(13,27,29,36)(14,17,25,16)(22,31,30,32)(23,35,26,33);(2,4)(5,6)(7,17)(8,13)(9,14)(10,15)(11,25)(12,19)(16,20)(18,32)(21,28)(22,23)(24,29)(26,30)(27,35)(31,34)(33,36);(5,8,10,24)(6,13,15,29)(7,18,20,34)(9,26,11,23)(12,27,28,36)(14,30,25,22)(16,31,17,32)(19,35,21,33)3053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16879);