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C3×#6029 #10597068

order600
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C5

Aliases

direct productC3×#6029

Splittings

derived, SylowC52 ⋊ C3×C8
HallC3×C52 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC3×C4C5⋊D5
commutator, hypocenterC52C3×C8
FrattiniC4C3×C5⋊D5
FittingC3×C4×C52C2
socle, prime radicalC2×C3×C52C4
cosocleC4×C52C2×C3
LCSG ▷ C52
UCSC1 ◁ C3×C4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 600

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#87764, C3×#87765, C3⋊#87764, …
maximal normal subgroup ofC3×#87764, C3×#87765, C3⋊#87764, …
maximal quotient ofC3×#87756, C2×C3×#6029, C9×#6029, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 49);