Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12916 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #120 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1850 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,25,20,24,39,50,21,26,40,51,18,35,38,52)(16,27,31,54,29,22,41,44,30,45,60,70,36,43,63,69)(17,23,33,47,32,48,61,72,34,49,62,73,37,46,64,71)(28,55,58,76,59,67,65,77,57,53,74,75,56,42,66,68);(14,16,19,31,20,29,39,41,21,30,40,60,18,36,38,63)(15,22,25,44,24,45,50,70,26,43,51,69,35,27,52,54)(17,28,33,58,32,59,61,65,34,57,62,74,37,56,64,66)(23,42,47,68,48,55,72,76,49,67,73,77,46,53,71,75);(14,17)(15,23)(16,28)(18,37)(19,33)(20,32)(21,34)(22,42)(24,48)(25,47)(26,49)(27,53)(29,59)(30,57)(31,58)(35,46)(36,56)(38,64)(39,61)(40,62)(41,65)(43,67)(44,68)(45,55)(50,72)(51,73)(52,71)(54,75)(60,74)(63,66)(69,77)(70,76)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5904);