Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ #459 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^178,e^c=ef,g^c=g^1781799 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37508055, #37508056, #37508066, … |
| maximal normal subgroup of | #37508055, #37508056, #37508066, … |
| maximal quotient of | #37508342, #37508356, #37508366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 745);