Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#88049 |
| Fitting | C4×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15753682, C8×#88049, #15753696, … |
| maximal normal subgroup of | #15753682, C8×#88049, #15753696, … |
| maximal quotient of | C4×#11718075, #15753544, #15753559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4328);