Finite Group Databasebeta

← Prev (#37551744) Next (#37551746) →

C4×#19154120 #37551745

order23276
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×#19154120

Splittings

Fitting, HallC4×C232 ⋊ C11
derived, SylowC232 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC4#19154120
commutator, hypocenterC232C4×C11
FrattiniC2C2×#19154120
FittingC4×C232C11
socle, cosocleC2×C232C2×C11
prime radicalC2×#19154120C2
LCSG ▷ C232
UCSC1 ◁ C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 2116

A minimal faithful permutation representation — 3 generators on 50 points:

(1,2,3,4)(6,7,8,10,13,14,19,22,9,12,16)(11,15,20,18,21,26,25,24,27,17,23)(29,30,31,33,36,37,42,45,32,35,39)(34,38,43,41,44,49,48,47,50,40,46);(28,29,30,32,31,34,35,40,33,37,38,44,39,45,46,50,36,41,42,47,43,48,49);(5,6,7,9,8,11,12,17,10,14,15,21,16,22,23,27,13,18,19,24,20,25,26)

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23276, 35);