Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#441 ⋊ C2 |
| Sylow | C3 ⋊ #2952 |
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 — 4 generators on 23 points:
(1,2)(8,12,14,10)(9,17,18,20)(11,19,13,21)(15,16,23,22);(4,6,7,5)(8,11,14,13)(9,16,18,22)(10,19,12,21)(15,20,23,17);(8,10,14,12)(9,15,18,23)(11,19,13,21)(16,20,22,17);(2,3)(4,5,7,6)(8,9,14,18)(10,17,12,20)(11,16,13,22)(15,21,23,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,d^2=g,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,h^d=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10948641, D3×#2952, C2×#79832, … |
| maximal normal subgroup of | #10948641, D3×#2952, C2×#79832, … |
| maximal quotient of | #10764673, #10764902, #10765044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12408);