Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Dic3×Q16 |
| Sylow | C3 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 245 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)(10,12,14,20)(11,15,17,24)(13,22,23,19)(16,25,21,18);(1,2)(10,11,14,17)(12,18,20,25)(13,21,23,16)(15,22,24,19);(4,5)(6,7,8,9);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#358, #10710408, Dic3×#362, … |
| maximal normal subgroup of | Dic3×#358, #10710408, Dic3×#362, … |
| maximal quotient of | C2×Q16×C3⋊C8, C2×#70903, C2×#70905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16448);