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D5×#66524 #16809663

order3330
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productD5×#66524
unambiguous semidirect productC5⋊(C2×#66524)

Splittings

derived, HallC5×C37 ⋊ C2×C9
HallC5×#66524 ⋊ C2
HallD5×C37 ⋊ C9
SylowC37 ⋊ C9×D5
SylowC5 ⋊ C2×#66524

Subgroups

subgroupG/H
center, Frattini, hypercenterC3D5×C37⋊C3
commutator, hypocenterC5×C37C2×C9
Fitting, socle, cosocleC3×C5×C37C2×C3
prime radicalC3×D5×C37C3
LCSG ▷ C5×C37
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 1665

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5)(7,8,10)(9,12,17)(11,15,14)(13,19,26)(16,21,23)(18,24,20)(22,29,33)(25,31,30)(27,34,28)(32,37,38)(35,39,36)(40,42,41)(43,44,46,45,47,49,48,50,51);(2,5)(3,4)(6,7,9,13,19,27,35,40,39,24,10,14,20,28,29,12,18,25,32,34,17,23,30,36,37,21,8,11,16,22,26,33,38,41,42,31,15)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD25×#66524, C5×D5×#66524, C5⋊D5×#66524, …
maximal normal subgroup ofC5×D5×#66524, C7×D5×#66524, D5×C11×#66524
maximal quotient ofD25×#66524, C5×D5×#66524, C5⋊D5×#66524, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3330, 3);