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C2×#16809824⋊C3 #34117682

order20130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×#16809824⋊C3
unambiguous semidirect product(C2×#16809824)⋊C3

Splittings

Fitting, socle, HallC2×C11×C61 ⋊ C3×C5
derived, HallC11×C61 ⋊ C2×C3×C5
HallC2×#16809824 ⋊ C3
HallC2×C11×C61⋊C3 ⋊ C5
Hall#16809824 ⋊ C2×C3
HallC11×C61⋊C3 ⋊ C2×C5
HallC2×C61⋊C3 ⋊ C11⋊C5
HallC61⋊C3 ⋊ C2×C11⋊C5
HallC2×C61 ⋊ C3×C11⋊C5
SylowC61 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ (C61⋊C3)⋊C5
SylowC11 ⋊ C2×(C61⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#16809824⋊C3
commutator, cosocle, hypocenterC11×C61C2×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C61C3×C5
LCSG ▷ C11×C61
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 74
transitive degreeμt(G) = 1342

A minimal faithful permutation representation — 2 generators on 74 points:

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

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20130, 11);