Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ #2052 |
262 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 69 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:
(1,2)(5,7)(8,11,12,9,14,16,13,17)(10,19,20,15,22,18,21,23);(8,10,14,22)(9,15,17,23)(11,18,16,19)(12,21,13,20);(2,3)(4,5)(6,7)(8,9)(10,18)(11,12)(13,16)(14,17)(15,20)(19,22)(21,23)Polycyclic presentation:
2^7,3|b^2=g,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2052, C2×#70264, #10823069, … |
| maximal normal subgroup of | D3×#2052, C2×#70264, #10823069, … |
| maximal quotient of | #10698880, #10698887, #10698908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2840);