Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
105 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 105 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4)(6,10)(7,14)(8,15)(11,12)(13,19)(16,20)(17,18);(2,3)(5,6,9,13)(7,10,16,19)(8,17,15,12)(11,20,18,14)Polycyclic presentation:
2^5,3,2^2|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=h,h^a=g,c^b=cd,d^b=de,g^f=h,h^f=gh29 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73134, #11714144, #11714145, … |
| maximal normal subgroup of | C2×#73134, #11714144, #11714145, … |
| maximal quotient of | #11711455, #11711459, #11711464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5710);