Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C19×#95 ⋊ C2 |
| Sylow | C19 ⋊ C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D19 |
| commutator | C2×C19 | C2×C42 |
| Fitting | C19×#95 | C2 |
| socle, cosocle | C23×C19 | C23 |
| prime radical | C23×D19 | C22 |
| hypercenter | #95 | D19 |
| hypocenter | C19 | C4×C22⋊C4 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #95 | |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=f,c^2=e,b^a=bd,g^c=g^18220 conjugacy classes — view the full character table.
| maximal subgroup of | #14562123, #14562125, #14562149, … |
| maximal normal subgroup of | #14562123, #14562125, #14562149, … |
| maximal quotient of | #95×Dic19, (C2×D19)⋊#95, #14561861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 396);