Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C26 |
| direct product | C31×#2614 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C22×D4×C31 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
782 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 232 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)(37,39)(40,41,44,47)(42,48,50,45)(43,46,52,51)(49,54,55,53);(33,35)(37,39)(40,42,44,50)(41,45,47,48)(43,49,52,55)(46,53,51,54);(32,33)(34,35)(36,37)(38,39)(40,41)(42,48)(43,51)(44,47)(45,50)(46,52)(49,53)(54,55);(40,43)(41,46)(42,49)(44,52)(45,53)(47,51)(48,54)(50,55)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#18225, C31×#18227, C31×#23905, … |
| maximal normal subgroup of | C31×#18225, C31×#18227, C31×#23905, … |
| maximal quotient of | C31×#14256, C31×#14263, C31×#14301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1346);