Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#8998 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #386 |
| prime radical | C13×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,23,27,29)(17,26,28,20)(18,21)(19,22)(24,25)(30,31)(32,38,40,45)(33,35)(34,37)(36,39,43,42)(41,44);(14,16,24,26,19,27,18,20)(15,17,25,23,22,28,21,29)(31,35)(34,41)(36,43)(39,42);(14,17)(15,20)(16,25)(18,29)(19,28)(21,27)(22,26)(23,24)(30,32)(31,36)(33,40)(34,42)(35,43)(37,45)(38,44)(39,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1986);