Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#3866)⋊C8 |
| Fitting | C2×C8×C37 ⋊ C4 |
| Sylow | C37 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^31,g^e=g^36184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#3866)⋊C8, #18010258, #18010261, … |
| maximal normal subgroup of | C2×(C2×#3866)⋊C8, #18010258, #18010261, … |
| maximal quotient of | #18009418, #18009419, #18009421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1414);