Finite Group Databasebeta

← Prev (#44568807) Next (#44568809) →

C3×C5×D11×C7⋊D7 #44568808

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC3×C5×D11×C7⋊D7

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derived, HallC72×C11 ⋊ C22×C3×C5
HallC5×C72×C11 ⋊ C22×C3
HallC3×C72×C11 ⋊ C22×C5
HallC3×C5×C72 ⋊ C2×D11
HallC5×C72 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C3×C7⋊D7
SylowC72 ⋊ C2×C3×C5×D11
HallC3×C11 ⋊ C2×C5×C7⋊D7
SylowC11 ⋊ C2×C3×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC3×C5D11×C7⋊D7
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C72×C11
UCSC1 ◁ C3×C5

400 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 33
transitive degreeμt(G) = 8085

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 510);