Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | Q8×D8×C19 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C2×D8×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×Q8×C19 ◁ G | |
404 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4)(5,8,7,6)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(1,5,3,7)(2,6,4,8);(9,10,11,12,13,14,15,16);(10,16)(11,15)(12,14)665 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12352, C19×#12356, C19×#12404, … |
| maximal normal subgroup of | C19×#12352, C19×#12356, C19×#12404, … |
| maximal quotient of | Q8×C19×#102, C4⋊C4×D8×C19, Q8×C19×#107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 2110);