Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33803 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C23×C13 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31,36,40)(32,41,42,58)(33,38,35,50)(34,46,49,60)(37,52,53,44)(39,45,57,48)(43,59,51,56)(47,54,61,55);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(32,42)(37,53)(41,58)(43,51)(44,52)(47,61)(54,55)(56,59);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,32)(31,37)(33,43)(34,47)(35,51)(36,42)(38,54)(39,56)(40,53)(41,46)(44,48)(45,52)(49,61)(50,55)(57,59)(58,60);(15,21)(19,22)(20,29)(27,28)(30,33,36,35)(31,38,40,50)(32,43,42,51)(34,45,49,48)(37,54,53,55)(39,46,57,60)(41,59,58,56)(44,47,52,61)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26791);