Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3199 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,21)(18,20)(19,23)(24,28)(25,27)(26,29)(30,31)(32,36)(33,38)(34,37)(35,40)(39,47)(41,49)(42,48)(43,51)(44,53)(45,54)(46,52)(50,57)(55,59)(56,60)(58,61);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32,35,43)(31,36,40,51)(33,44,45,41)(34,42,47,57)(37,48,39,50)(38,53,54,49)(46,58,59,56)(52,61,55,60);(16,23)(19,22)(24,29)(26,28)(31,37)(34,47)(36,48)(38,52)(39,40)(42,57)(46,59)(49,60)(50,51)(53,61)(54,55)(56,58);(15,20)(19,22)(21,27)(26,28)(30,33)(31,38)(32,41)(34,46)(35,45)(36,49)(37,52)(39,55)(40,54)(42,56)(43,44)(47,59)(48,60)(50,61)(51,53)(57,58);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(33,45)(38,54)(41,44)(46,59)(49,53)(52,55)(56,58)(60,61)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53995);