Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62823 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6538 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,21)(16,24,25,22)(17,27,26,23)(18,19,28,29)(31,35)(33,40)(36,41)(39,44);(15,21)(16,25)(18,28)(23,27)(32,38)(36,41)(39,44)(43,45);(14,16,20,25)(15,22,21,24)(17,18,26,28)(19,27,29,23)(30,31,34,35)(32,36,38,41)(33,37,40,42)(39,43,44,45);(14,17,20,26)(15,23,21,27)(16,18,25,28)(19,24,29,22);(14,18)(15,19)(16,26)(17,25)(20,28)(21,29)(22,27)(23,24)(30,32)(31,36)(33,39)(34,38)(35,41)(37,43)(40,44)(42,45);(14,19)(15,18)(16,27)(17,24)(20,29)(21,28)(22,26)(23,25)(30,33)(31,37)(32,39)(34,40)(35,42)(36,43)(38,44)(41,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55811);