Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D13 |
| commutator, socle, cosocle | C23×C13 | C23 |
| Fitting | C2×C13×C4⋊C4 | C2 |
| prime radical | C22×D52 | C2 |
| hypercenter | C2×C4⋊C4 | D13 |
| hypocenter | C13 | #394 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 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) = 416 |
Polycyclic presentation:
2^6,13|b^2=e,c^2=f,b^a=be,c^a=cd,g^a=g^12,c^b=cf142 conjugacy classes — view the full character table.
| maximal subgroup of | #13112838, #13112840, #13113765, … |
| maximal normal subgroup of | #13112838, #13112840, #13113765, … |
| maximal quotient of | #13113076, #13113078, #13113084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 618);