Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C13×#120 ⋊ C2 |
| Sylow | C13 ⋊ #2847 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C2×C13×#120 | C2 |
| hypercenter | C2×#120 | D13 |
| hypocenter | C13 | #2847 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
1224 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=e,b^a=be,c^a=cf,d^a=dg,h^b=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15897101, #15897105, #15898549, … |
| maximal normal subgroup of | #15897101, #15897105, #15898549, … |
| maximal quotient of | #15794077, #15794132, #15794135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12790);