Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×Dic12 |
| Sylow | C3 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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:
(3,4,5)(10,12,19,23,14,21,13,20)(11,15,22,25,17,24,16,18);(1,2)(4,5)(10,11,14,17)(12,18,21,25)(13,22,19,16)(15,23,24,20);(6,7,8,9);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10689754, #10689756, #10689782, … |
| maximal normal subgroup of | #10689754, #10689756, #10689782, … |
| maximal quotient of | C2×C8×Dic12, C2×#68086, C2×#68056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11048);