Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C179 ⋊ #421 |
154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,179|a^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^178,c^b=cf,d^b=df1802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37508964, #37508965, #37508969, … |
| maximal normal subgroup of | #37508964, #37508965, #37508969, … |
| maximal quotient of | #37507387, #37507391, #37507395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 566);