Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C2×C59×#2028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C23×C4×C59 ◁ G | |
1238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(3,4,6,8)(5,9,10,7)(11,12)(13,19)(14,22)(15,18)(16,20)(17,23)(21,26)(24,25);(3,5,6,10)(4,7,8,9)(14,23)(16,25)(17,22)(20,24);(11,13,15,21)(12,16,18,25)(14,24,23,20)(17,26,22,19)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16448);