Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2020 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
342 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 59 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)(28,29,34,39)(30,40,44,51)(31,45,49,54)(32,38,33,37)(35,43,52,42)(36,48,55,47)(41,56,58,50)(46,53,57,59);(25,27)(28,30)(29,35)(31,46)(32,43)(33,42)(34,44)(36,53)(37,51)(38,40)(39,52)(41,48)(45,56)(47,58)(49,57)(50,54)(55,59);(28,31,34,49)(29,36,39,55)(30,41,44,58)(32,48,33,47)(35,50,52,56)(37,54,38,45)(40,53,51,59)(42,46,43,57)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7399, C23×#7401, C23×#12111, … |
| maximal normal subgroup of | C23×#7399, C23×#7401, C23×#12111, … |
| maximal quotient of | C23×#9976, C23×#9979, C23×#9989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 752);