Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4716 |
| Sylow | C3 ⋊ C2×#441 |
480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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) = 384 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5)(6,7,8,9)(12,20)(15,24)(18,25)(21,23);(1,2)(10,12,19,23,14,20,13,21)(11,15,22,25,17,24,16,18);(4,5)(10,11,14,17)(12,18,20,25)(13,22,19,16)(15,23,24,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690604, #10690606, #10690632, … |
| maximal normal subgroup of | #10690604, #10690606, #10690632, … |
| maximal quotient of | C2×#68084, C2×#68087, C2×#68089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11077);