Finite Group Databasebeta

← Prev (#91872) Next (#91874) →

Cayley diagram

C2×#6728 #91873

order480
isoclinismisoclinic class of #6728
automorphismAut(G) = D4×S5 (order 960) · Inn(G) = S5 · Out(G) = D4
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productC2×#6728

Subgroups

subgroupG/H
center, Fitting, socle, hypercenterC22S5
commutator, cosocle, hypocenterSL(2,𝔽5)C22
FrattiniC2C2×S5
prime radicalC2×SL(2,𝔽5)C2
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C22

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 2 generators on 50 points:

(3,46,19,29,9,24,38,14)(4,6,5,16,12,7,15,17)(8,44,20,27,21,42,41,28)(10,39,43,33,11,40,45,31)(13,32,25,36,26,30,49,37)(18,23,34,47,35,22,50,48);(1,2)(3,21,20,39,16,9,8,41,40,17)(4,10,23,24,15,12,11,22,46,5)(6,7)(13,49,43,42,29,26,25,45,44,14)(18,50,31,30,38,35,34,33,32,19)(27,28)(36,37)(47,48)

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#6728, C4⋊#6728, #11751510, …
maximal normal subgroup ofC4×#6728, C4⋊#6728, #11751510, …
maximal quotient ofC4×#6728, C4⋊#6728, #11751517, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 949);