Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C179 ⋊ #405 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^2=e,d^2=f,g^a=g^178,c^b=cf,g^b=g^1781820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37508754, #37508756, #37508799, … |
| maximal normal subgroup of | #37508754, #37508756, #37508799, … |
| maximal quotient of | M16×C179⋊C8, #37507284, #37507287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 507);