Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C2×C42 |
| direct product | C31×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C25×C31 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 992 |
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)(32,33)(34,38)(35,36)(37,39)(40,41,44,45)(42,46,47,43)(48,49,51,53)(50,54,55,52);(33,36)(34,39)(41,45)(43,46)(48,49,51,53)(50,52,55,54);(32,34)(33,37)(35,39)(36,38)(40,42)(41,43)(44,47)(45,46)(48,49)(50,52)(51,53)(54,55);(32,33)(34,37)(35,36)(38,39)(40,43)(41,42)(44,46)(45,47)(48,50)(49,52)(51,55)(53,54)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#12188, C31×#12264, C31×#36725, … |
| maximal normal subgroup of | C31×#12188, C31×#12264, C31×#36725, … |
| maximal quotient of | C31×#14366, C31×#14481, C31×#14577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1468);