Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#5388 |
275 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,4,5,6)(7,9,16)(8,19,21,12,13,22)(11,17,18)(14,20);(7,8,11,12)(9,14,17,20)(10,13,15,19)(16,22,18,21);(1,2)52 conjugacy classes — view the full character table.
| maximal subgroup of | #11711148, C4×#5388, #11712579, … |
| maximal normal subgroup of | #11711148, C4×#5388, #11712579, … |
| maximal quotient of | C2×#226⋊C8, C2×#73009, #11711859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17892);