Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4816 |
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ C2×#470 |
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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:
(3,4,5)(6,7)(8,9)(10,12,14,19)(11,16,15,22)(13,21,20,18)(17,24,23,25);(6,7,8,9)(11,15)(12,18)(13,20)(16,24)(19,21)(22,25);(1,2)(4,5)(7,9)(10,11)(12,16)(13,17)(14,15)(18,25)(19,22)(20,23)(21,24);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4816, #10801841, #10801877, … |
| maximal normal subgroup of | C4×#4816, #10801841, #10801877, … |
| maximal quotient of | C2×#68449, C2×#68501, C2×#68455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11375);