Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#33324 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C59 | C24 |
| commutator | C2 | C22×C4×C8×C59 |
| Frattini, cosocle | C2×C8 | C24×C59 |
| socle | C22×C59 | C23×C8 |
| prime radical | C24×C59 | C2×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C59 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 95 points:
(5,6,8,13,9,14,18,26,10,12,19,24,20,25,30,34)(7,11,16,22,17,23,29,33,15,21,27,31,28,32,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2,3,4)(5,7)(6,11)(8,16)(9,17)(10,15)(12,21)(13,22)(14,23)(18,29)(19,27)(20,28)(24,31)(25,32)(26,33)(30,35)(34,36);(7,15)(11,21)(16,27)(17,28)(22,31)(23,32)(29,35)(33,36);(6,12)(11,21)(13,24)(14,25)(22,31)(23,32)(26,34)(33,36)8024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26312);