Finite Group Databasebeta

← Prev (#11924833) Next (#11924835) →

C3×#87721 #11924834

order1200
isoclinismisoclinic class of #87721
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87721

Splittings

HallC3×C25 ⋊ SD16
SylowC25 ⋊ C3×SD16

Subgroups

subgroupG/H
centerC2×C3C22⋊D25
commutator, cosocleC4×C25C22×C3
FrattiniC4×C5C2×C3×D5
FittingC3×D4×C25C2
socleC2×C3×C5C22⋊D5
prime radicalC3×C5×D4D5
hypercenterC3×D4D25
hypocenterC25C3×SD16
LCSG ▷ C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 600

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3)(4,17,25,13,20,10,9,28,14,12,19,5,22,27,7,11,18,15,26,16,6,24,8,21,23)(30,33)(31,36)(34,35);(5,7)(6,10)(8,13)(9,16)(11,19)(12,18)(14,15)(17,23)(20,24)(21,25)(22,27)(26,28)(29,30,32,35)(31,33,36,34)

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 44);