Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
267 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,4)(5,6,8);(1,2)(3,4)(6,7)(9,10,11,13,12,14,15,16)Polycyclic presentation:
2^5,3,2^2|a^2=c,c^2=e,b^a=bd,f^a=f^2,g^a=h,h^a=g,g^f=h,h^f=gh56 conjugacy classes — view the full character table.
| maximal subgroup of | #11711009, #11711010, #11711019, … |
| maximal normal subgroup of | #11711009, #11711010, #11711019, … |
| maximal quotient of | #11711009, #11711010, D4⋊(A4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5717);