Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#11855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
324 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)(16,22,24,19)(17,20)(18,21)(23,28,25,27)(26,29)(30,31)(32,42)(33,39)(34,49)(35,52)(36,41)(37,44)(38,47)(40,51)(43,55)(45,61)(46,57)(48,58)(50,59)(53,54)(56,60);(14,16)(15,19)(17,25)(18,24)(20,28)(21,22)(23,26)(27,29)(30,32)(31,37)(33,44)(34,50)(35,53)(36,46)(38,57)(39,54)(40,59)(41,56)(42,49)(43,47)(45,51)(48,60)(52,55)(58,61);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,33,35,47,36,48,51,34)(31,38,40,39,41,49,52,58)(32,43,45,44,46,50,53,60)(37,54,55,57,56,61,59,42)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4843);