Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
163 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 163 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)(6,27,30,11,22,36)(7,17,34,16,31,33)(8,20,10)(12,13,35,15,25,29)(14,26)(18,32)(19,28);(5,6,10,15)(7,11,16,12)(8,19,21,14)(9,22,24,13)(17,28,31,26)(18,27,32,25)(20,30,23,29)(33,36,34,35)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=c,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,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×#73077, #11712736, #11712737, … |
| maximal normal subgroup of | C2×#73077, #11712736, #11712737, … |
| maximal quotient of | #11711108, #11711117, #11711120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5653);