Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C283 ⋊ C2 |
| Sylow | C283 ⋊ #577 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4528 |
Polycyclic presentation:
2^6,283|a^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^282,e^b=ef,d^c=df2419 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49133022, #49133025, #49133034, … |
| maximal normal subgroup of | #49133022, #49133025, #49133034, … |
| maximal quotient of | #49129787, #49129791, #49129854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1360);