Finite Group Databasebeta

← Prev (#27211871) Next (#27211873) →

C2×#20269517 #27211872

order13420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×#20269517

Splittings

Fitting, socleC2×C11×C61 ⋊ C2×C5
derived, HallC11×C61 ⋊ C22×C5
Hall#16809821 ⋊ C22
HallC2×C11×D61 ⋊ C5
HallC2×D61 ⋊ C11⋊C5
SylowC61 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#20269517
commutator, cosocle, hypocenterC11×C61C22×C5
FrattiniC1G
Fitting, socleC2×C11×C61C2×C5
LCSG ▷ C11×C61
UCSC1 ◁ C2

40 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:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13420, 64);