Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C179 ⋊ #410 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=e,c^2=f,b^a=bd,d^a=df,g^a=g^178,e^b=ef1802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507120, #37507121, #37507129, … |
| maximal normal subgroup of | #37507120, #37507121, #37507129, … |
| maximal quotient of | #37507314, #37507321, #37507324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 523);