Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
209 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 36 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) = 96 |
A minimal faithful permutation representation — 2 generators on 16 points:
(5,6,8)(9,10,12,14)(11,16,15,13);(1,2,3,4)(6,7)(10,13)(11,15)(14,16)Polycyclic presentation:
2^5,3,2^2|a^2=c,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=h,h^a=g,d^b=de,g^f=h,h^f=gh38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73147, #11712600, #11712603, … |
| maximal normal subgroup of | C2×#73147, #11712600, #11712603, … |
| maximal quotient of | #11711012, #11711020, #11711024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5723);