Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 3072 |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#237 |
| Fitting | C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,13)(10,14);(8,10,11,14)(9,12,13,15);(2,3)(8,9)(10,12)(11,13)(14,15);(4,5,6,7)60 conjugacy classes — view the full character table.
| maximal subgroup of | #68165, #68166, #68173, … |
| maximal normal subgroup of | #68165, #68166, #68173, … |
| maximal quotient of | C4×#877, C4×#67⋊C4, C4×#886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1095);