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C3×C4⋊#1035 #11924898

order1200
isoclinismisoclinic class of #87735
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4⋊#1035
unambiguous semidirect productC4⋊(C3×#1035)

Splittings

FittingC3×C4×C25 ⋊ C4
HallC3×C25 ⋊ C4⋊C4
SylowC25 ⋊ C3×C4⋊C4

Subgroups

subgroupG/H
centerC2×C3C2×#1035
commutatorC2×C25C2×C3×C4
FrattiniC2×C5C2×C3×AGL(1,𝔽5)
FittingC3×C4×C25C4
socleC2×C3×C5C2×AGL(1,𝔽5)
prime radicalC2×C3×D25C22
cosocleC2×D25C22×C3
hypercenterC3×C4#1035
hypocenterC25C3×C4⋊C4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2×C3 ◁ C3×C4

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 300

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 108);