Finite Group DatabasebetaFinite Group Databasebeta| order | 24256 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4⋊Q8×C379 ⋊ C2 |
| Sylow | C379 ⋊ #541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D379 |
| commutator, socle, cosocle | C22×C379 | C24 |
| Fitting | C4⋊Q8×C379 | C2 |
| prime radical | C22×D379 | C23 |
| hypercenter | C4⋊Q8 | D379 |
| hypocenter | C379 | #541 |
| LCS | G ▷ C22×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12128 |
Polycyclic presentation:
2^6,379|a^2=e,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^378,g^c=g^3782668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24256, 1160);