Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1395 |
162 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,9,19,10,20,7,17)(5,11,14,27,15,28,12,16)(8,22,23,25,24,18,21,33)(13,26,30,34,31,35,29,32);(2,3)(4,5,8,13)(6,16,18,32)(7,14,21,30)(9,12,23,29)(10,15,24,31)(11,25,26,17)(19,28,33,35)(20,27,22,34)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,e^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dfg,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1395, C2×#67692, #10710180, … |
| maximal normal subgroup of | D3×#1395, C2×#67692, #10710180, … |
| maximal quotient of | #10682152, #10682188, #10682191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 268);