Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
95 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,2,4)(5,7,10,18)(6,11,14,28)(8,20,23,36)(9,25,21,17)(12,30,31,35)(13,32,24,27)(15,33,34,19)(16,29,26,22);(2,3)(5,6,10,14)(7,15,18,34)(8,19,23,33)(9,24,21,13)(11,26,28,16)(12,29,31,22)(17,35,25,30)(20,32,36,27)Polycyclic presentation:
2^5,3,2^2|a^2=e,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×#73136, #11714144, #11714146, … |
| maximal normal subgroup of | C2×#73136, #11714144, #11714146, … |
| maximal quotient of | #11711456, #11711460, #11711465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5712);