Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #127×C293 ⋊ C2 |
| Sylow | C293 ⋊ #540 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #127×C293 | C2 |
| hypercenter | #127 | D293 |
| hypocenter | C293 | #540 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #127 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^292,g^c=g^2922066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49168981, #49168983, #49169026, … |
| maximal normal subgroup of | #49168981, #49168983, #49169026, … |
| maximal quotient of | #49161393, #49161422, #49161481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1153);