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C3×C11×#168 #13050302

order1320
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C3×C8×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×#168

Splittings

derived, SylowC5 ⋊ C3×C8×C11
HallC3×C5×C11 ⋊ C8
HallC5×C11 ⋊ C3×C8
HallC3×C5 ⋊ C8×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11D5
commutator, hypocenterC5C3×C8×C11
FrattiniC4C3×D5×C11
FittingC3×C4×C5×C11C2
socle, prime radicalC2×C3×C5×C11C4
cosocleC4×C5C2×C3×C11
LCSG ▷ C5
UCSC1 ◁ C3×C4×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 1320

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 6);