Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#21477 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C59 | #120 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C2×C59 | C4×#120 |
| prime radical | C59×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C59 ◁ C22×C8×C59 ◁ G | |
1290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,8,11,7,12,6,22)(3,13,16,9,17,26,23,27)(4,18,19,21,20,10,24,5)(14,28,30,25,31,15,29,32)(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);(1,3)(2,9)(4,14)(5,15)(6,23)(7,17)(8,16)(10,25)(11,26)(12,27)(13,22)(18,32)(19,30)(20,31)(21,28)(24,29);(1,4)(2,10)(3,14)(5,11)(6,24)(7,20)(8,19)(9,25)(12,18)(13,28)(15,26)(16,30)(17,31)(21,22)(23,29)(27,32);(1,5,8,18,7,21,6,10)(2,4,11,19,12,20,22,24)(3,15,16,32,17,28,23,25)(9,14,26,30,27,31,13,29)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14465);