Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5239 |
| Sylow | C3 ⋊ C2×#452 |
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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)(10,12,14,20)(11,16,18,24)(13,19,21,25)(15,22,17,23);(1,2)(11,15)(13,21)(16,22)(17,18)(19,25)(23,24);(1,2)(4,5)(7,9)(10,11,14,18)(12,16,20,24)(13,15,21,17)(19,22,25,23);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10691492, #10691494, #10800810, … |
| maximal normal subgroup of | #10691492, #10691494, #10800810, … |
| maximal quotient of | C2×#71889, C2×#71887, C2×#71885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16659);