Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#12616 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×C42 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C22×C59 | C2×#97 |
| prime radical | C24×C59 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 79 points:
(1,2)(3,4)(5,6,9,15,10,12,18,19,11,7,13,16,8,14,17,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(2,4)(6,12,7,14)(9,13)(15,20,16,19)(17,18);(5,7,9,16,10,14,18,20,11,6,13,15,8,12,17,19)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5604);