Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #2367 |
632 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,14,15,18)(13,17,16,19);(8,9,10,11)(13,16)(17,19);(2,3)(4,6,7,5)(13,16)(14,18);(2,3)(4,5,7,6)(9,11)(12,13)(14,17)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^b=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10817475, #10817477, #10817490, … |
| maximal normal subgroup of | #10817475, #10817477, #10817490, … |
| maximal quotient of | #10716635, #10716729, #10716756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15531);