Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×Q16 ⋊ D3 |
102 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 102 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)(5,6,9,12)(7,14,16,20)(8,17,15,11)(10,18,19,13);(2,3)(6,10)(7,13)(8,15)(11,20)(12,19)(14,17)(16,18)Polycyclic presentation:
2^5,3,2^2|b^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×#73135, #11714144, #11714146, … |
| maximal normal subgroup of | C2×#73135, #11714144, #11714146, … |
| maximal quotient of | #11711454, #11711458, #11711463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5711);