Finite Group Databasebeta

← Prev (#44538283) Next (#44538285) →

C2×C5×C11⋊D143 #44538284

order31460
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C5×C11⋊D143
unambiguous semidirect product(C2×C13)⋊(C5×C11⋊D11)

Splittings

Fitting, socleC2×C5×C112×C13 ⋊ C2
derived, HallC112×C13 ⋊ C22×C5
HallC5×C112×C13 ⋊ C22
HallC5×C112 ⋊ C2×D13
SylowC112 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×C11⋊D11
SylowC13 ⋊ C2×C5×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊D143
commutator, cosocle, hypocenterC112×C13C22×C5
FrattiniC1G
Fitting, socleC2×C5×C112×C13C2
LCSG ▷ C112×C13
UCSC1 ◁ C2×C5

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 15730

A minimal faithful permutation representation — 3 generators on 42 points:

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

Conjugacy classes & character table

7880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 224);