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C3×#87724 #11924837

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

Aliases

direct productC3×#87724

Splittings

FittingC3×Q8×C25 ⋊ C2
HallC3×C25 ⋊ SD16
SylowC25 ⋊ C3×SD16

Subgroups

subgroupG/H
centerC2×C3C22⋊D25
commutator, cosocleC4×C25C22×C3
FrattiniC4×C5C2×C3×D5
FittingC3×Q8×C25C2
socleC2×C3×C5C22⋊D5
prime radicalC3×D100C2
hypercenterC3×Q8D25
hypocenterC25C3×SD16
LCSG ▷ C4×C25 ▷ C2×C25 ▷ C25
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q8

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

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, 47);