Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73011 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
105 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,7,8)(2,6,4)(9,11,18,22,13,20,12,19)(10,14,21,24,16,23,15,17);(2,5)(3,7)(6,8)(9,10,13,16)(11,17,20,24)(12,21,18,15)(14,22,23,19)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=cd,c^2=d,f^2=h,g^2=h,b^a=bc,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh37 conjugacy classes — view the full character table.
| maximal subgroup of | #11711455, #11711456, #11711459, … |
| maximal normal subgroup of | #11711455, #11711456, #11711459, … |
| maximal quotient of | #11711071, #11711182, C2×#73015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5591);