Finite Group DatabasebetaFinite Group Databasebeta| order | 29888 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #126×C467 ⋊ C2 |
| Sylow | C467 ⋊ #538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D467 |
| commutator, socle, cosocle | C22×C467 | C24 |
| Fitting | #126×C467 | C2 |
| hypercenter | #126 | D467 |
| hypocenter | C467 | #538 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C22 ◁ #126 | |
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7472 |
Polycyclic presentation:
2^6,467|b^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^466,c^b=ce,g^d=g^4663284 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29888, 1138);