Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #396 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D19 |
| commutator, socle, cosocle | C23×C19 | C23 |
| Fitting | C2×C4⋊C4×C19 | C2 |
| prime radical | C23×D19 | C22 |
| hypercenter | C2×C4⋊C4 | D19 |
| hypocenter | C19 | #396 |
| LCS | G ▷ C23×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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=de,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#396, C2×#11926466, #14566871, … |
| maximal normal subgroup of | D19×#396, C2×#11926466, #14566871, … |
| maximal quotient of | #14561877, #14561879, #14561881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 471);