Finite Group DatabasebetaFinite Group Databasebeta| order | 24256 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #126×C379 ⋊ C2 |
| Sylow | C379 ⋊ #529 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D379 |
| commutator, socle, cosocle | C22×C379 | C24 |
| Fitting | #126×C379 | C2 |
| prime radical | #27131304 | C2 |
| hypercenter | #126 | D379 |
| hypocenter | C379 | #529 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ #126 | |
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12128 |
Polycyclic presentation:
2^6,379|b^2=f,d^2=e,b^a=be,c^a=cf,g^b=g^378,g^c=g^378,g^d=g^3782674 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24256, 1082);