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×#61015 |
| 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 | |
1768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 45 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)(30,31,34,38)(32,39,35,36)(33,41,43,37)(40,44,42,45);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32,34,35)(31,36,38,39)(33,42,43,40)(37,45,41,44);(16,23)(19,22)(24,29)(26,28)(31,36)(32,35)(37,44)(38,39)(40,42)(41,45);(15,20)(19,22)(21,27)(26,28)(30,33,34,43)(31,37,38,41)(32,40,35,42)(36,44,39,45);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(33,43)(37,41)(40,42)(44,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54003);