Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#13125 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C59 | C2×D4 |
| commutator | C2×C4 | C22×C8×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C22×C59 | C8×D4 |
| prime radical | C2×#41×C59 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C59 ◁ C22×C16×C59 ◁ G | |
324 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2)(3,4)(5,6,11,17,10,15,8,26,12,18,28,14,9,16,20,33)(7,19,24,34,23,31,27,32,25,30,35,36,22,13,21,29)(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);(5,7,20,21,9,22,28,35,12,25,8,27,10,23,11,24)(6,13,26,34,16,30,17,29,18,31,33,36,15,19,14,32);(2,4)(5,8,9,11,12,20,10,28)(6,14,15,33,18,17,16,26)(7,21,22,35,25,27,23,24)(13,29,19,34,31,32,30,36)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6113);