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) = 96 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,28,85,20,52,45,8,33,54,3,31,30)(2,83,69,37,80,96,15,39,65,9,46,90)(4,63,78,58,57,81,26,24,88,22,62,92)(5,6,74,18,55,66,7,32,87,27,19,73)(10,48,60,44,36,70,41,12,89,38,79,53)(11,56,72,35,49,67,13,82,29,42,50,94)(14,77,75,40,47,68,16,84,71,21,43,93)(17,51,61,23,59,95,34,76,86,25,64,91);(1,2,8,15)(3,16,20,14)(4,21,26,40)(5,13,7,11)(6,29,32,72)(9,34,37,17)(10,25,41,23)(12,45,48,30)(18,44,27,38)(19,53,55,70)(22,42,58,35)(24,60,63,89)(28,65,33,69)(31,75,52,71)(36,78,79,88)(39,81,83,92)(43,66,47,73)(46,74,80,87)(49,54,50,85)(51,67,76,94)(56,86,82,61)(57,90,62,96)(59,68,64,93)(77,91,84,95)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^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×#73138, #11714153, #11714154, … |
| maximal normal subgroup of | C2×#73138, #11714153, #11714154, … |
| maximal quotient of | #11711455, #11711460, #11711462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5714);