Finite Group Databasebeta

← Prev (#37555665) Next (#37555667) →

C7×C3⋊D561 #37555666

order23562
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊D561
unambiguous semidirect productC3⋊(C7×D561)
unambiguous semidirect productC11⋊(C7×C3⋊D51)
unambiguous semidirect productC17⋊(C7×C3⋊D33)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, HallC32×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C3⋊D3
HallC32×C7×C17 ⋊ D11
HallC32×C7×C11 ⋊ D17
HallC11×C17 ⋊ C7×C3⋊D3
HallC32×C17 ⋊ C7×D11
HallC7×C17 ⋊ C3⋊D33
HallC32×C11 ⋊ C7×D17
HallC7×C11 ⋊ C3⋊D51
HallC32×C7 ⋊ D187
SylowC17 ⋊ C7×C3⋊D33
SylowC11 ⋊ C7×C3⋊D51
SylowC32 ⋊ C7×D187

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D561
commutator, cosocle, hypocenterC32×C11×C17C2×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C32×C11×C17
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 11781

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

5901 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 60);