Finite Group Databasebeta

← Prev (#44394645) Next (#44394647) →

C7×D115⋊(C3⋊D3) #44394646

order28980
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC7×D115⋊(C3⋊D3)
unambiguous semidirect productD115⋊(C7×C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C7×C23 ⋊ C22
derived, HallC32×C5×C23 ⋊ C22×C7
HallC32×C7×C23 ⋊ C2×D5
HallC5×C7×C23 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D23
HallC32×C23 ⋊ C2×C7×D5
HallC7×C23 ⋊ D5×C3⋊D3
HallC5×C23 ⋊ C2×C7×C3⋊D3
HallC32×C7 ⋊ D5×D23
HallC32×C5 ⋊ C2×C7×D23
HallC5×C7 ⋊ C3⋊D3×D23
SylowC23 ⋊ C7×D5×C3⋊D3
SylowC32 ⋊ C7×D5×D23
SylowC5 ⋊ C7×C3⋊D3×D23

Subgroups

subgroupG/H
center, hypercenterC7D115⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C23C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C32×C5×C23
UCSC1 ◁ C7

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 7245

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

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

Conjugacy classes & character table

2016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 315);