Finite Group Databasebeta

← Prev (#44538204) Next (#44538206) →

C2×C13⋊((C11⋊C5)⋊D11) #44538205

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

Aliases

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

Splittings

Fitting, socleC2×C112×C13 ⋊ C2×C5
derived, HallC112×C13 ⋊ C22×C5
HallC11×C13×C11⋊C5 ⋊ C22
HallC2×C11⋊D143 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D13
SylowC112 ⋊ C2×C5×D13
SylowC13 ⋊ C2×(C11⋊C5)⋊D11

Subgroups

subgroupG/H
center, hypercenterC2C13⋊((C11⋊C5)⋊D11)
commutator, cosocle, hypocenterC112×C13C22×C5
FrattiniC1G
Fitting, socleC2×C112×C13C2×C5
LCSG ▷ C112×C13
UCSC1 ◁ C2

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1430

A minimal faithful permutation representation — 2 generators on 37 points:

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

Conjugacy classes & character table

1016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 145);