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C5×C3⋊D3×D143 #38788264

order25740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C3⋊D3×D143

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derived, HallC32×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ C2×C3⋊D3
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×C3⋊D3
HallC32×C13 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ C3⋊D3×D11
HallC5×C11 ⋊ C3⋊D3×D13
HallC32×C5 ⋊ C2×D143
SylowC13 ⋊ C5×C3⋊D3×D11
SylowC11 ⋊ C5×C3⋊D3×D13
SylowC32 ⋊ C2×C5×D143

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D3×D143
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 35
transitive degreeμt(G) = 6435

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

2190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 495);