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Cayley diagram

C5×#984 #91943

order480
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#984

Subgroups

subgroupG/H
center, socleC2×C5C2×S4
commutator, cosocle, hypocenterSL(2,𝔽3)C22×C5
FrattiniC2C2×C5×S4
FittingC5×#41D3
prime radicalC5×#41⋊C3C2
hypercenterC4×C5S4
LCSG ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C5 ◁ C4×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5)(6,17,23,19,9,33,11,34,21,8,22,35)(7,24,29,16,13,36,15,30,27,12,28,37)(10,18,20,32)(14,25,26,31);(6,7,11,15)(8,16,19,12)(9,14,22,26)(10,13,20,28)(17,31,34,25)(18,30,32,24)(21,29,23,27)(33,36,35,37)

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11751620, #11751622, #11751627, …
maximal normal subgroup of#11751620, #11751622, #11751627, …
maximal quotient ofC5×#5386, C5×#5388, C5×C4⋊#226, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1019);