Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5051 |
| Sylow | C3 ⋊ C2×#467 |
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5)(7,9)(10,13,15,12)(11,17,19,25)(14,21,24,22)(16,18,20,23);(1,2)(6,7)(8,9)(10,12)(11,16)(13,15)(14,21)(17,23)(18,25)(19,20)(22,24);(4,5)(7,9)(10,11,15,19)(12,20,13,16)(14,23,24,18)(17,21,25,22);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10694700, #10694702, #10694710, … |
| maximal normal subgroup of | #10694700, #10694702, #10694710, … |
| maximal quotient of | C2×#71101, C2×#71133, C2×#71103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15305);