Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C13 · Schur multiplier (H2) = C220 |
| direct product | C13×#63103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C26 |
| commutator, Frattini, cosocle | C2 | C27×C13 |
| socle | C2×C13 | C27 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ G | |
59452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 7 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,21)(18,23)(19,22)(20,26)(25,36)(27,37)(28,33)(29,34)(30,35)(31,38)(32,40)(39,44)(41,43)(42,45);(14,16)(15,20)(17,25)(18,27)(19,26)(21,31)(22,24)(23,32)(28,38)(29,39)(30,40)(33,36)(34,42)(35,37)(41,45)(43,44);(14,17)(15,21)(16,25)(18,29)(19,28)(20,31)(22,33)(23,34)(24,36)(26,38)(27,39)(30,41)(32,42)(35,43)(37,44)(40,45);(17,28)(21,33)(25,38)(29,41)(31,36)(34,43)(39,45)(42,44);(16,26)(20,24)(25,38)(27,40)(31,36)(32,37)(39,45)(42,44);(15,22)(20,24)(21,33)(23,35)(31,36)(32,37)(34,43)(42,44);(14,18,19,30)(15,23,22,35)(16,27,26,40)(17,29,28,41)(20,32,24,37)(21,34,33,43)(25,39,38,45)(31,42,36,44)1690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56091);