Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C293 ⋊ C2 |
| Sylow | C293 ⋊ #540 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #125×C293 | C2 |
| hypercenter | #125 | D293 |
| hypocenter | C293 | #540 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #125 | |
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,g^a=g^292,c^b=ce,g^b=g^292,g^c=g^2922066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49168989, #49168991, #49169030, … |
| maximal normal subgroup of | #49168989, #49168991, #49169030, … |
| maximal quotient of | #49161395, #49161424, #49161476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1155);