Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
132 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,3,4)(5,21,23)(6,27,32,11,22,36)(7,17,34,16,31,33)(8,20,10)(12,13,35,15,25,30)(14,26)(18,29)(19,28);(5,6,7,12,10,15,16,11)(8,19,17,26,21,14,31,28)(9,22,18,25,24,13,29,27)(20,32,33,35,23,30,34,36)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=c,d^2=h,f^2=h,g^2=h,b^a=bd,e^a=e^2,f^a=gh,g^a=fh,d^b=dh,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73075, #11712685, #11712686, … |
| maximal normal subgroup of | C2×#73075, #11712685, #11712686, … |
| maximal quotient of | #11711084, #11711096, #11711097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5651);