Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C23×C4 |
| direct product | C71×#24637 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C71 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| prime radical | C22×D4×C71 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C71 ◁ C4×C4⋊C4×C71 ◁ G | |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,3,4)(5,6)(7,11)(8,9)(10,12)(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);(6,9)(10,11)(13,14,18,21)(15,22,24,27)(16,20,17,25)(19,26,28,23);(2,4)(13,15,18,24)(14,19,21,28)(16,23,17,26)(20,27,25,22);(5,7,8,12)(6,10,9,11)(13,16,18,17)(14,20,21,25)(15,23,24,26)(19,27,28,22)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 17625);