Finite Group DatabasebetaFinite Group Databasebeta| order | 24448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #399×C191 ⋊ C2 |
| Sylow | C191 ⋊ #2397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D191 |
| commutator, socle, cosocle | C23×C191 | C24 |
| Fitting | #399×C191 | C2 |
| hypercenter | #399 | D191 |
| hypocenter | C191 | #2397 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ #399 | |
840 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12224 |
Polycyclic presentation:
2^7,191|a^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^190,h^d=h^1902134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24448, 7790);