Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C37 ⋊ #433 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^31,c^b=cf,g^b=g^36,g^e=g^36118 conjugacy classes — view the full character table.
| maximal subgroup of | D37⋊#433, C2×#14558558, #18011277, … |
| maximal normal subgroup of | D37⋊#433, C2×#14558558, #18011277, … |
| maximal quotient of | #18010315, #18010325, #18010384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1574);