Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2337 |
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^16,c^b=ce364 conjugacy classes — view the full character table.
| maximal subgroup of | #16931610, #16931614, #16931624, … |
| maximal normal subgroup of | #16931610, #16931614, #16931624, … |
| maximal quotient of | #16955600, #16955659, #16955664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7323);