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C2×C5×C11×C61⋊C3 #34117679

order20130
isoclinismisoclinic class of C61⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×C61⋊C3
unambiguous semidirect product(C2×C5×C61)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C61)⋊C3

Splittings

Fitting, socle, HallC2×C5×C11×C61 ⋊ C3
derived, SylowC61 ⋊ C2×C3×C5×C11
HallC5×C11×C61 ⋊ C2×C3
HallC2×C11×C61 ⋊ C3×C5
HallC11×C61 ⋊ C2×C3×C5
HallC2×C5×C61 ⋊ C3×C11
HallC5×C61 ⋊ C2×C3×C11
HallC2×C61 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C61⋊C3
commutator, cosocle, hypocenterC61C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C61C3
LCSG ▷ C61
UCSC1 ◁ C2×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 6710

A minimal faithful permutation representation — 2 generators on 79 points:

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

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20130, 8);