Finite Group Databasebeta

← Prev (#10660561) Next (#10660563) →

C3×#41955 #10660562

order768
nilpotency class2
isoclinismisoclinic class of #40484
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C28

Aliases

direct productC3×#41955

Subgroups

subgroupG/H
center, socleC23×C3C25
commutator, Frattini, cosocleC23C25×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

2752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 192

A minimal faithful permutation representation — 5 generators on 23 points:

(1,2,3)(4,5,6,7)(8,9,12,11)(10,14,15,13);(9,11)(13,14)(16,17)(18,19)(20,21)(22,23);(4,5)(6,7)(10,15)(13,14)(17,21)(18,22);(8,10)(9,13)(11,14)(12,15)(16,18,20,22)(17,19,21,23);(8,11,12,9)(10,14,15,13)(16,19)(17,22)(18,21)(20,23)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD3×#41955, #72253603
maximal subgroup ofD3×#41955, #72253603, C3×#7918389
maximal normal subgroup ofD3×#41955, #72253603, C3×#7918389
maximal quotient ofC3×#758017

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 34943);