Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#11025 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C2×D4 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C23×C59 | C4×D4 |
| prime radical | C22×#135×C59 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ C23×C8×C59 ◁ G | |
1334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2)(3,4)(5,6)(7,8)(9,10,13,18,15,11,14,17)(12,16,22,20,23,19,21,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(2,4)(9,11)(10,15)(12,20)(13,17)(14,18)(16,21)(19,22)(23,24);(6,8)(9,12)(10,16)(11,19)(13,22)(14,21)(15,23)(17,24)(18,20)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4013);