Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4808 |
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ C2×#452 |
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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)(10,12,14,20)(11,16,15,18)(13,22,21,19)(17,24,23,25);(1,2)(6,8,9,7)(11,15)(12,19)(13,21)(16,24)(18,25)(20,22);(4,5)(6,7)(8,9)(10,11)(12,18)(13,17)(14,15)(16,20)(19,24)(21,23)(22,25);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10800816, C4×#4808, #10800890, … |
| maximal normal subgroup of | #10800816, C4×#4808, #10800890, … |
| maximal quotient of | C2×#68326, C2×#68330, C2×#68319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11370);