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C2×C13×C5⋊(C11⋊D11) #44538289

order31460
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C13×C5⋊(C11⋊D11)
unambiguous semidirect product(C2×C5)⋊(C13×C11⋊D11)
unambiguous semidirect product(C2×C11)⋊(C13×D55)

Splittings

Fitting, socleC2×C5×C112×C13 ⋊ C2
derived, HallC5×C112 ⋊ C22×C13
HallC5×C112×C13 ⋊ C22
HallC112×C13 ⋊ C2×D5
SylowC112 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C11⋊D11
SylowC5 ⋊ C2×C13×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C13C5⋊(C11⋊D11)
commutator, cosocle, hypocenterC5×C112C22×C13
FrattiniC1G
Fitting, socleC2×C5×C112×C13C2
LCSG ▷ C5×C112
UCSC1 ◁ C2×C13

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:

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

Conjugacy classes & character table

7904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 229);