Finite Group Databasebeta

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Cayley diagram

C5×#836 #91079

order480
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#836

Splittings

HallC3×C5 ⋊ #101
SylowC3 ⋊ C5×#101

Subgroups

subgroupG/H
centerC2×C5#217
commutatorC22×C3C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC2×C3×C5×Q8C2
socleC2×C3×C5C22⋊C4
prime radicalC22×C3×C5C2×C4
cosocleC2×C3×C4C22×C5
hypercenterC2×C5×Q8D3
hypocenterC3C5×#101
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×Q8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746012, #11746014, #11746015, …
maximal normal subgroup of#11746012, #11746014, #11746015, …
maximal quotient ofC5×#4528, C5×#4530, C5×#4543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 155);