Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ #2328 |
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,15,16,13)(14,18,19,17);(2,3)(8,9,10,11)(12,14,16,19)(13,17,15,18);(4,6,7,5)(12,13,16,15)(14,18,19,17);(4,5,7,6)(9,11)(13,15)(17,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=eg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690689, #10690690, #10690692, … |
| maximal normal subgroup of | #10690689, #10690690, #10690692, … |
| maximal quotient of | #10716446, #10716491, #10716496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14905);