Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#427 ⋊ C2 |
| Sylow | C3 ⋊ C4×#135 |
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17);(2,3)(4,6,7,5);(2,3)(8,10)(9,14)(11,18)(12,21)(13,19)(15,22)(16,23)(17,20);(4,5,7,6)(8,9)(10,17)(11,15)(12,20)(13,16)(14,18)(19,22)(21,23)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^2,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10710410, #10710415, #10710434, … |
| maximal normal subgroup of | #10710410, #10710415, #10710434, … |
| maximal quotient of | #10764564, #10764716, #10764935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11741);