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D5×#66526 #16809676

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

Aliases

direct productD5×#66526
unambiguous semidirect productC5⋊(C2×#66526)

Splittings

Fitting, socle, derived, HallC5×C37 ⋊ C2×C9
HallC5×#66526 ⋊ C2
HallD5×C37 ⋊ C9
SylowC37 ⋊ C9×D5
SylowC5 ⋊ C2×#66526

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C37C2×C9
prime radicalD5×C37⋊C3C3
cosocleC5×C37⋊C3C2×C3
LCSG ▷ C5×C37
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 185

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD25×#66526, C5×D5×#66526, C5⋊D5×#66526, …
maximal normal subgroup ofC5×D5×#66526, C7×D5×#66526, D5×C11×#66526
maximal quotient ofD25×#66526, C5×D5×#66526, C5⋊D5×#66526, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3330, 16);