Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#8603 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #380 |
| prime radical | C24×C13 | C4⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
368 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20,18,21,24,27)(16,19,23,26,22,25,28,29)(30,31)(32,40)(33,44,46,37)(34,47)(35,39)(36,42)(38,48)(41,54,56,52)(43,53)(45,51,60,59)(49,55,58,61)(50,57);(14,16)(15,19)(17,23)(18,22)(20,26)(21,25)(24,28)(27,29)(30,32,34,42,35,43,48,57)(31,36,38,40,39,50,47,53)(33,41,45,55,46,56,60,61)(37,49,51,52,44,58,59,54);(16,22)(19,25)(23,28)(26,29)(30,33)(31,37)(32,41)(34,45)(35,46)(36,49)(38,51)(39,44)(40,52)(42,55)(43,56)(47,59)(48,60)(50,58)(53,54)(57,61)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1591);