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C3×#87765 #11925053

order1200
isoclinismisoclinic class of #1044
automorphism?
homologyAbelianization (H1) = C3×C16 · Schur multiplier (H2) = C5

Aliases

direct productC3×#87765

Splittings

derived, SylowC52 ⋊ C3×C16
HallC3×C52 ⋊ C16

Subgroups

subgroupG/H
center, hypercenterC3×C4#1044
commutator, hypocenterC52C3×C16
FrattiniC4C3×#1044
FittingC3×C4×C52C4
socle, prime radicalC2×C3×C52C8
cosocle#6029C2×C3
LCSG ▷ C52
UCSC1 ◁ C3×C4

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 263);