Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C23×C4 |
| direct product | C71×#22761 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C71 | C22×D4 |
| commutator | C2×C4 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ C4×C4⋊C4×C71 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 18176 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,3,4)(5,6)(7,10)(8,12)(9,11)(14,19)(17,26)(20,21)(22,27)(23,25)(24,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(5,7,9,8)(6,10,11,12)(13,14)(15,20)(16,24)(17,27)(18,22)(19,26)(21,25)(23,28);(5,8,9,7)(6,10,11,12)(13,15,18,16)(14,20,22,24)(17,23,26,25)(19,21,27,28);(13,16,18,15)(14,21,22,28)(17,23,26,25)(19,20,27,24)4118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 15749);