Finite Group Databasebeta

← Prev (#14579642) Next (#14579644) →

C7×C22⋊(C31⋊C3) #14579643

order2604
isoclinismisoclinic class of C22⋊(C31⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×C22⋊(C31⋊C3)
unambiguous semidirect productC22⋊(C7×C31⋊C3)
unambiguous semidirect productC31⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C7×C31 ⋊ C3
derived, HallC22×C31 ⋊ C3×C7
HallC7×C31 ⋊ A4
SylowC31 ⋊ C7×A4
HallC22×C7 ⋊ C31⋊C3
SylowC22 ⋊ C7×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C22⋊(C31⋊C3)
commutator, cosocle, hypocenterC22×C31C3×C7
FrattiniC1G
Fitting, socleC22×C7×C31C3
LCSG ▷ C22×C31
UCSC1 ◁ C7

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 868

A minimal faithful permutation representation — 2 generators on 42 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C22⋊((C31⋊C3)⋊C5), C5×C7×C22⋊(C31⋊C3), C49×C22⋊(C31⋊C3), …
maximal normal subgroup ofC7×C22⋊((C31⋊C3)⋊C5), C5×C7×C22⋊(C31⋊C3), C49×C22⋊(C31⋊C3), …
maximal quotient ofC5×C7×C22⋊(C31⋊C3), C49×C22⋊(C31⋊C3), C7×C22⋊#10620252, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2604, 54);