Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#11040 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #127 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #392 |
| prime radical | C2×C59×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
1278 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)(7,16)(8,21)(9,26)(10,14)(11,15)(12,18)(13,24)(17,34)(19,29)(20,28)(22,33)(23,32)(25,31)(27,35)(30,36)(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);(5,7)(6,12)(8,22)(9,19)(10,18)(11,20)(13,30)(14,28)(15,29)(16,26)(17,23)(21,27)(24,35)(25,36)(31,34)(32,33);(5,8)(6,13)(7,17)(9,23)(10,24)(11,25)(12,27)(14,31)(15,32)(16,33)(18,22)(19,36)(20,35)(21,26)(28,30)(29,34)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4028);