Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
227 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(6,8)(9,23,18,16,19,24,13,14,20,10,11,22)(12,15,17,21);(1,2,3,4)(5,6)(7,8)(11,17)(12,19)(14,21)(15,23)(18,20)(22,24)Polycyclic presentation:
2^4,3,2^3|a^2=c,b^2=h,f^2=h,g^2=h,b^a=bd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711057, #11711058, #11711214, … |
| maximal normal subgroup of | #11711057, #11711058, #11711214, … |
| maximal quotient of | #11711014, #11711031, #11711033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5727);