Finite Group DatabasebetaFinite Group Databasebeta| order | 24896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×Q8×C389 ⋊ C2 |
| Sylow | C389 ⋊ #548 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D389 |
| commutator, socle, cosocle | C22×C389 | C24 |
| Fitting | C22×Q8×C389 | C2 |
| hypercenter | C22×Q8 | D389 |
| hypocenter | C389 | #548 |
| LCS | G ▷ C22×C389 ▷ C389 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
290 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12448 |
Polycyclic presentation:
2^6,389|b^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^388,d^b=de3905 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24896, 1210);