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C3×#88036 #11927937

order1248
isoclinismisoclinic class of #261
automorphism?
homologyAbelianization (H1) = C3×C32 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88036

Splittings

derived, SylowC13 ⋊ C3×C32
HallC3×C13 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C8#261
commutator, hypocenterC13C3×C32
FrattiniC8C3×#261
FittingC3×C8×C13C4
socle, prime radicalC2×C3×C13C16
cosocle#6090C2×C3
LCSG ▷ C13
UCSC1 ◁ C3×C8

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 1248

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3)(5,6,7,9)(8,11,12,16)(10,14,15,13)(17,18,19,23,20,24,27,33,21,25,28,34,30,36,39,43,22,26,29,35,31,37,40,44,32,38,41,45,42,46,47,48);(4,5,8,11,15,9,13,14,6,10,16,12,7)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 49);