Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C241 ⋊ #362 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^240,c^b=cef,d^b=df,e^b=ef,g^b=g^2402416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #362×D241, C2×#29507534, #44509191, … |
| maximal normal subgroup of | #362×D241, C2×#29507534, #44509191, … |
| maximal quotient of | #44505416, #44505464, #44505495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 366);