Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #102 |
127 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 127 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,3,4,2)(5,6,10,12,8,11,7,9)(14,15)(16,17,18);(1,2,4,3)(6,9)(7,10)(11,12)(13,14,15)(17,18)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=cde,d^2=e,b^a=bd,d^a=de,g^a=g^2,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10590281, #10590282, #10590293, … |
| maximal normal subgroup of | #10590281, #10590282, #10590293, … |
| maximal quotient of | #10589082, #10589091, #10589094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 212);