Finite Group Databasebeta

← Prev (#91878) Next (#91880) →

Cayley diagram

C2×#6732 #91879

order480
isoclinismisoclinic class of SL(2,𝔽5)
automorphismAut(G) = D4×S5 (order 960) · Inn(G) = A5 · Out(G) = C2×D4
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productC2×#6732

Splittings

derivedSL(2,𝔽5) ⋊ C22

Subgroups

subgroupG/H
center, Fitting, hypercenterC2×C4A5
commutator, hypocenterSL(2,𝔽5)C22
Frattini, cosocleC2C22×A5
socleC22C2×A5
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C2×C4

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×GL(2,𝔽5), #11751499, #11751513, …
maximal normal subgroup ofC2×GL(2,𝔽5), #11751499, #11751513, …
maximal quotient ofC4×#6732, C22⋊#6732, C4⋊#6732, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 955);