Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1773 |
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 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) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,10,11,17,12,16,19,23)(9,14,18,21,15,22,13,20);(2,3)(4,5,6,7)(8,9)(10,14)(11,18)(12,15)(13,19)(16,22)(17,21)(20,23);(9,13,15,18)(10,16)(14,21,22,20)(17,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=de,d^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10710457, #10710459, #10710464, … |
| maximal normal subgroup of | #10710457, #10710459, #10710464, … |
| maximal quotient of | #10686353, #10686357, #10686361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2405);