Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C293 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #11924078 |
| commutator, hypocenter | C293 | C64 |
| Fitting | C16×C293 | C4 |
| socle, prime radical | C2×C293 | C32 |
| cosocle | #22627530 | C2 |
| LCS | G ▷ C293 | |
| UCS | C1 ◁ C16 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
Polycyclic presentation:
2^6,293|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^138,g^b=g^2921232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34036968, D293⋊C64, #49173954, … |
| maximal normal subgroup of | C2×#34036968, D293⋊C64, #49173954, … |
| maximal quotient of | #49173600, C2×#34036968 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1388);