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Cayley diagram

C5⋊#994 #91965

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

Aliases

unambiguous semidirect productC5⋊#994
unambiguous semidirect product#4149⋊C3

Splittings

Hall#4149 ⋊ C3
SylowC5 ⋊ #994

Subgroups

subgroupG/H
center, FrattiniC2C2×D5×A4
commutator, cosocle, hypocenterC5×Q8C22×C3
FittingC5×#41C2×C3
socleC2×C5C22×A4
hypercenterC4D5×A4
LCSG ▷ C5×Q8
UCSC1 ◁ C2 ◁ C4

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:

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

Polycyclic presentation:

2^2,3,2^2,5,2|a^2=g,b^2=g,d^2=g,e^2=g,b^a=bg,f^a=f^4,d^c=de,e^c=d,e^d=eg

Conjugacy classes & character table

47 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11751629, #11751630, #11751631, …
maximal normal subgroup of#11751629, #11751630, #11751631, …
maximal quotient ofSL(2,𝔽3)×Dic10, #65908⋊C3, C4⋊(C5⋊(#41⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1041);