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C2×C5×#66526 #16809677

order3330
isoclinismisoclinic class of #66526
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#66526

Splittings

Fitting, socle, HallC2×C5×C37 ⋊ C9
derived, SylowC37 ⋊ C2×C5×C9
HallC5×C37 ⋊ C2×C9
HallC2×C37 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5#66526
commutator, hypocenterC37C2×C5×C9
FrattiniC1G
Fitting, socleC2×C5×C37C9
prime radicalC2×C5×C37⋊C3C3
cosocleC37⋊C3C2×C3×C5
LCSG ▷ C37
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 370

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C25×#66526, C5×D5×#66526, C2×C52×#66526, …
maximal normal subgroup ofC2×C25×#66526, C2×C52×#66526, C2×C5×C7×#66526, …
maximal quotient ofC2×C25×#66526, C5×D5×#66526, C2×C52×#66526, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3330, 17);