Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4⋊C4×Dic13 |
| Sylow | C13 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic13×#324, #15753435, #15755578, … |
| maximal normal subgroup of | Dic13×#324, #15753435, #15755578, … |
| maximal quotient of | C2×#95×Dic13, C4×C4⋊C4×Dic13, C2×#13113061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6847);