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Cayley diagram

C22×C5×SL(2,𝔽3) #92052

order480
isoclinismisoclinic class of SL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×SL(2,𝔽3)

Splittings

Fitting, HallC22×C5×Q8 ⋊ C3
derivedQ8 ⋊ C22×C3×C5
SylowC22×Q8 ⋊ C3×C5

Subgroups

subgroupG/H
center, socle, hypercenterC23×C5A4
commutator, cosocle, hypocenterQ8C22×C3×C5
FrattiniC2C22×C5×A4
FittingC22×C5×Q8C3
LCSG ▷ Q8
UCSC1 ◁ C23×C5

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 2 generators on 17 points:

(3,4)(5,6,7,8,9)(11,12,14)(15,17,16);(1,2)(10,14,13,16)(11,17,15,12)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×#859, C5×#5419, C5×#5420, …
maximal normal subgroup ofC2×C5×#859, C5×#5419, C5×#5420, …
maximal quotient ofC2×C4×C5×SL(2,𝔽3), C5×D4×SL(2,𝔽3), C5×Q8×SL(2,𝔽3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1128);