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Cayley diagram

C5×#994 #92055

order480
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#994

Splittings

Fitting, HallC5×H(5,𝔽2) ⋊ C3
SylowH(5,𝔽2) ⋊ C3×C5

Subgroups

subgroupG/H
center, socleC2×C5C22×A4
commutator, cosocle, hypocenterQ8C22×C3×C5
FrattiniC2C22×C5×A4
FittingC5×H(5,𝔽2)C3
hypercenterC5×Q8A4
LCSG ▷ Q8
UCSC1 ◁ C2×C5 ◁ C5×Q8

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

derived subgroup of#72277270, D5×GL(2,𝔽3)⋊A4, #72277286, …
maximal subgroup ofC5×#5428, C5×#5429, #11752147, …
maximal normal subgroup ofC5×#5428, C5×#5429, #11752147, …
maximal quotient ofC5×#520⋊C3, C5×C4⋊(#41⋊C3), C5×Q8×SL(2,𝔽3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1131);