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×#61010 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1700 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)(32,41)(33,45)(34,39)(35,37)(36,42)(38,47)(40,49)(43,51)(44,50)(46,54)(48,55)(52,56)(53,59)(57,61)(58,60);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32)(31,36)(33,46)(34,42)(35,44)(37,52)(38,54)(39,41)(40,50)(43,47)(45,51)(48,58)(49,56)(53,60)(55,61)(57,59);(16,23)(19,22)(24,29)(26,28)(31,37)(32,42)(35,49)(36,50)(38,53)(39,40)(41,52)(43,46)(45,55)(48,59)(51,60)(54,61);(15,20)(19,22)(21,27)(26,28)(30,33)(31,38)(32,43)(34,47)(35,48)(36,51)(37,53)(39,45)(40,55)(41,54)(42,46)(44,57)(49,59)(50,60)(52,61)(56,58);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(33,47)(38,45)(43,46)(48,59)(51,54)(53,55)(57,58)(60,61)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53998);