Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C293 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #11924078 |
| commutator, hypocenter | C293 | C4×C16 |
| Frattini | C2×C4 | C2×#11924078 |
| Fitting | C2×C8×C293 | C4 |
| socle, prime radical | C22×C293 | C2×C8 |
| cosocle | C2×#14556873 | C22 |
| LCS | G ▷ C293 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
Polycyclic presentation:
2^6,293|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^138,g^b=g^292,g^c=g^2921232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#14556880, #49173696, #14556880⋊C16, … |
| maximal normal subgroup of | C16×#14556880, #49173696, #14556880⋊C16, … |
| maximal quotient of | C8×#17989805, #49173700, #49173824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1435);