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 ⋊ #2129 |
238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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:
(1,2,3)(4,7,9,20)(5,11,13,28)(6,15,17,18)(8,19,23,35)(10,24,25,26)(12,27,21,34)(14,30,29,32)(16,31,22,33);(2,3)(4,6,9,17)(5,10,13,25)(7,18,20,15)(8,22,23,16)(11,26,28,24)(12,29,21,14)(19,31,35,33)(27,30,34,32);(4,5)(6,14,17,29)(7,11)(8,21,23,12)(9,13)(10,16)(15,30,18,32)(19,34,35,27)(20,28)(22,25)(24,31)(26,33)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,c^2=g,d^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=dg,e^b=efg,h^b=h^2,e^d=eg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10710736, #10710737, #10710741, … |
| maximal normal subgroup of | #10710736, #10710737, #10710741, … |
| maximal quotient of | #10704302, #10704351, #10704483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2635);