Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#3020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,21)(18,30)(19,22)(20,26)(23,33)(25,41)(27,38)(28,39)(29,36)(31,35)(32,37)(34,42)(40,43)(44,45);(14,16)(15,20)(17,25)(18,31)(19,27)(21,34)(22,35)(23,38)(24,30)(26,33)(28,44)(29,43)(32,42)(36,45)(37,40)(39,41);(14,17,19,29)(15,21,22,36)(16,25,27,43)(18,32,33,28)(20,34,35,45)(23,39,30,37)(24,40,38,41)(26,44,31,42);(15,22)(20,35)(21,36)(23,30)(24,38)(34,45)(37,39)(40,41)377 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 1752);