Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2239 |
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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 — 3 generators on 35 points:
(1,2)(4,6,8,24,9,15,21,17)(5,10,12,31,13,26,23,27)(7,20,22,25,19,34,28,16)(11,30,18,32,29,33,35,14);(7,19)(11,29)(14,32)(16,25)(18,35)(20,34)(22,28)(30,33);(2,3)(4,5,9,13)(6,14,15,32)(7,18,19,35)(8,23,21,12)(10,25,26,16)(11,28,29,22)(17,30,24,33)(20,27,34,31)Polycyclic presentation:
2^7,3|a^2=g,c^2=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,e^b=eg,d^c=dg,e^c=efg,f^c=fg,h^c=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | #10708518, #10708519, #10708524, … |
| maximal normal subgroup of | #10708518, #10708519, #10708524, … |
| maximal quotient of | #10711515, #10711756, #10712225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1693);