Finite Group DatabasebetaFinite Group Databasebeta| order | 23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C373 ⋊ C2 |
| Sylow | C373 ⋊ #563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D373 |
| commutator, socle, cosocle | C22×C373 | C24 |
| Fitting | #125×C373 | C2 |
| prime radical | C2×D1492 | C22 |
| hypercenter | #125 | D373 |
| hypocenter | C373 | #563 |
| LCS | G ▷ C22×C373 ▷ C373 | |
| UCS | C1 ◁ C22 ◁ #125 | |
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 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) = 11936 |
Polycyclic presentation:
2^6,373|a^2=e,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,g^a=g^372,c^b=cef,d^b=de,g^d=g^3722623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23872, 1303);