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C3×#87709 #11924795

order1200
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C3×C16 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87709

Splittings

derived, SylowC25 ⋊ C3×C16
HallC3×C25 ⋊ C16

Subgroups

subgroupG/H
center, hypercenterC3×C4#1035
commutator, hypocenterC25C3×C16
FrattiniC4×C5C3×AGL(1,𝔽5)
FittingC3×C4×C25C4
socle, prime radicalC2×C3×C5#170
cosocle#6014C2×C3
LCSG ▷ C25
UCSC1 ◁ C3×C4

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 1200

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 5);