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C3×D5×C11×C61 #34117689

order20130
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C61 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C11×C61
unambiguous semidirect productC5⋊(C2×C3×C11×C61)

Splittings

Fitting, socle, HallC3×C5×C11×C61 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C11×C61
HallC5×C11×C61 ⋊ C2×C3
HallC3×C5×C61 ⋊ C2×C11
HallC5×C61 ⋊ C2×C3×C11
HallC3×C5×C11 ⋊ C2×C61
HallC5×C11 ⋊ C2×C3×C61
HallC3×C5 ⋊ C2×C11×C61

Subgroups

subgroupG/H
center, hypercenterC3×C11×C61D5
commutator, cosocle, hypocenterC5C2×C3×C11×C61
FrattiniC1G
Fitting, socleC3×C5×C11×C61C2
LCSG ▷ C5
UCSC1 ◁ C3×C11×C61

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 80
transitive degreeμt(G) = 10065

A minimal faithful permutation representation — 2 generators on 80 points:

(2,3)(4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66)(67,68,69,70,71,72,73,74,75,76,77)(78,79,80);(1,2,4,5,3)

Conjugacy classes & character table

8052 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20130, 18);