Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | M16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=e,d^2=f,g^a=g^155,c^b=cf,g^b=g^138,g^d=g^292,g^e=g^292770 conjugacy classes — view the full character table.
| maximal subgroup of | #49174542, #49174544, #49174561, … |
| maximal normal subgroup of | #49174542, #49174544, #49174561, … |
| maximal quotient of | M16×#14556880, #49173983, #49173990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1515);