Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C2×C42 |
| direct product | C31×#2835 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C24×C31 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
380 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(33,36)(37,39)(40,41)(42,44)(43,45)(46,47)(48,49,52,54)(50,51,53,55);(34,38)(37,39)(40,41,43,45)(42,44,47,46)(48,50)(49,51)(52,53)(54,55);(32,33,35,36)(34,37,38,39)(40,42,43,47)(41,44,45,46)(48,51)(49,53)(50,54)(52,55);(32,34)(33,37)(35,38)(36,39)(40,41)(42,46)(43,45)(44,47)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#12139, C31×#12233, C2×C31×#2835, … |
| maximal normal subgroup of | C31×#12139, C31×#12233, C2×C31×#2835, … |
| maximal quotient of | C31×#14627, C31×#14635, C31×#14647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1567);