Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #123×C293 ⋊ C2 |
| Sylow | C293 ⋊ #562 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #123×C293 | C2 |
| hypercenter | #123 | D293 |
| hypocenter | C293 | #562 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #123 | |
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|c^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^b=g^292,g^c=g^2922063 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #562×D293, C2×#34036876, #49172920, … |
| maximal normal subgroup of | #562×D293, C2×#34036876, #49172920, … |
| maximal quotient of | #49161931, #49161932, #49161933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1296);