Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32×C59 · Schur multiplier (H2) = C2 |
| direct product | C59×#7510 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C59 | C22 |
| commutator | C2 | C4×C32×C59 |
| Frattini, cosocle | C2×C32 | C22×C59 |
| socle, prime radical | C22×C59 | C2×C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C59 ◁ G | |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 2 generators on 127 points:
(5,6,7,13,8,14,17,31,9,15,18,32,21,34,37,53,10,16,19,33,22,35,38,54,24,36,40,55,43,56,57,66,11,12,20,27,23,28,39,47,25,29,41,48,44,50,58,62,26,30,42,49,45,51,59,63,46,52,60,64,61,65,67,68)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127);(1,2,3,4)(6,12)(13,27)(14,28)(15,29)(16,30)(31,47)(32,48)(33,49)(34,50)(35,51)(36,52)(53,62)(54,63)(55,64)(56,65)(66,68)9440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 498);