Finite Group DatabasebetaFinite Group Databasebeta| order | 24896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #117×C389 ⋊ C2 |
| Sylow | C389 ⋊ #540 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D389 |
| commutator, socle, cosocle | C22×C389 | C24 |
| Fitting | #117×C389 | C2 |
| hypercenter | #117 | D389 |
| hypocenter | C389 | #540 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ #117 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12448 |
Polycyclic presentation:
2^6,389|b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^388,c^b=ce3902 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24896, 1154);