Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
193 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,27,19,3,17,30)(2,25,24,7,18,32)(4,29,6,13,16,12)(5,14)(8,21,23,11,9,31)(10,22)(15,26)(20,28);(1,2)(3,11,12,7)(4,15)(5,18)(6,8)(9,20)(10,17)(13,22,27,26)(14,21,28,25)(16,24)(19,23)(29,31,30,32)Polycyclic presentation:
2^4,3,2^3|a^2=c,f^2=h,g^2=h,b^a=bd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,c^b=ch,f^e=g,g^e=fgh,g^f=gh31 conjugacy classes — view the full character table.
| maximal subgroup of | #11711508, #11711509, #11711510, … |
| maximal normal subgroup of | #11711508, #11711509, #11711510, … |
| maximal quotient of | #11711017, #11711018, #11711029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5732);