Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4873 |
| Sylow | C3 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 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)(6,8,9,7)(10,12)(11,15)(13,21)(14,19)(16,25)(17,23)(18,20)(22,24);(1,2)(6,8,9,7)(12,18)(13,20)(15,22)(16,24)(19,21)(23,25);(4,5)(6,7,9,8)(10,11,14,17)(12,15,19,23)(13,16,20,24)(18,22,21,25);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710395, #10710405, #10710444, … |
| maximal normal subgroup of | #10710395, #10710405, #10710444, … |
| maximal quotient of | C2×#68557, C2×#68560, C2×#68564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11710);