Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1979 |
276 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3)(8,11,13,24,14,25,12,23)(9,16,26,36,17,32,18,22)(10,19,27,37,20,34,21,35)(15,28,30,38,31,39,29,33);(4,6,7,5)(8,10,12,21,14,20,13,27)(9,15,18,29,17,31,26,30)(11,19,23,35,25,34,24,37)(16,28,22,33,32,39,36,38);(2,3)(4,5,7,6)(8,9,13,18,14,17,12,26)(10,15,21,30,20,31,27,29)(11,22,24,32,25,36,23,16)(19,33,35,28,34,38,37,39)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,c^2=eg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712292, #10712293, #10712299, … |
| maximal normal subgroup of | #10712292, #10712293, #10712299, … |
| maximal quotient of | #10694118, #10694128, #10694382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2480);