Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ C4×#108 |
228 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(4,6,7,5);(1,2,3)(8,10,11,20,13,21,12,19)(9,14,15,22,17,23,16,18);(4,5,7,6)(8,9,12,16,13,17,11,15)(10,18,20,14,21,22,19,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,f^2=g,b^a=bd,d^b=dg,e^b=eg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10705614, #10705618, #10705622, … |
| maximal normal subgroup of | #10705614, #10705618, #10705622, … |
| maximal quotient of | #10686367, #10686371, #10686375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1492);