Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C23 |
| direct product | C2×C59×D64 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | D32 |
| commutator, Frattini, cosocle | C32 | C23×C59 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C4×C59 ◁ C2×C8×C59 ◁ C2×C16×C59 ◁ C2×C32×C59 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 125 points:
(1,2)(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);(3,4)(5,10)(6,21)(7,25)(8,28)(9,15)(11,16)(12,17)(13,22)(14,26)(18,38)(19,40)(20,32)(23,56)(24,54)(27,58)(29,42)(30,41)(31,49)(33,48)(34,51)(35,44)(36,57)(37,47)(39,55)(43,59)(45,53)(46,52)(50,63)(60,66)(61,65)(62,64);(4,10)(5,16)(6,17)(7,22)(8,26)(11,12)(13,38)(14,40)(15,32)(18,48)(19,51)(20,44)(21,29)(23,57)(24,47)(25,30)(27,55)(28,31)(33,53)(34,52)(35,37)(36,59)(39,63)(41,42)(43,49)(45,46)(50,66)(54,61)(56,60)(58,62)(64,65)4130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6726);