Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 64 points:
(1,24,26)(2,46,38,8,25,56)(3,57,47,14,45,64)(4,20,52,15,41,51)(5,23,7)(9,49,60,10,54,62)(11,55,13,29,37,31)(12,30)(16,63,18,39,44,32)(17,40)(19,33,61,28,35,59)(21,42)(22,43)(34,36)(48,58)(50,53);(1,2,7,13)(3,8,18,31)(4,19,15,10)(5,22,24,12)(6,25,27,11)(9,32,28,14)(16,43,45,30)(17,46,48,29)(20,36,41,50)(21,35,42,49)(23,38,26,37)(33,40,54,58)(34,39,53,57)(44,56,47,55)(51,61,52,62)(59,63,60,64)Polycyclic presentation:
2^4,3,2^3|a^2=h,c^2=dh,d^2=h,f^2=h,g^2=h,b^a=bc,c^a=cd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,c^b=cd,d^b=dh,f^e=g,g^e=fgh,g^f=gh25 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73140, #11714153, #11714155, … |
| maximal normal subgroup of | C2×#73140, #11714153, #11714155, … |
| maximal quotient of | #11711456, #11711459, #11711463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5716);