Finite Group Databasebeta

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C5×A5×C37⋊C3 #45686527

order33300
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×A5×C37⋊C3
unambiguous semidirect productC37⋊(C3×C5×A5)
unambiguous semidirect product(C5×C37)⋊(C3×A5)
unambiguous semidirect product(C37×A5)⋊(C3×C5)
unambiguous semidirect product(C5×C37×A5)⋊C3

Splittings

FittingC5×C37 ⋊ C3×A5
socleC5×C37×A5 ⋊ C3
derivedC37×A5 ⋊ C3×C5
SylowC37 ⋊ C3×C5×A5

Subgroups

subgroupG/H
center, hypercenterC5A5×C37⋊C3
commutator, hypocenterC37×A5C3×C5
FrattiniC1G
FittingC5×C37C3×A5
socleC5×C37×A5C3
cosocleC37C3×C5×A5
LCSG ▷ C37×A5
UCSC1 ◁ C5

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 925

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 800);