Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
129 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 129 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:
(2,4)(5,27,32,11,8,26,17,22,21,6,31,36,10,12,30,24,20,28,7,35,19,14,15,34)(9,13,16,23,18,25,29,33);(1,2,3,4)(8,18)(9,20)(12,25)(13,27)(15,29)(16,31)(19,21)(22,33)(23,35)(26,28)(30,32)(34,36)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=c,c^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 | C2×#73122, #11712701, #11712702, … |
| maximal normal subgroup of | C2×#73122, #11712701, #11712702, … |
| maximal quotient of | #11711086, #11711087, #11711098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5698);