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C3×C11⋊#170 #13050338

order1320
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊#170
unambiguous semidirect productC11⋊(C3×#170)

Splittings

derived, HallC5×C11 ⋊ C3×C8
HallC3×C5×C11 ⋊ C8
HallC3×C11 ⋊ #170
HallC3×C5 ⋊ C11⋊C8
SylowC11 ⋊ C3×#170
SylowC5 ⋊ C3×C11⋊C8

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C8
FrattiniC2C3×C11⋊AGL(1,𝔽5)
Fitting, socle, prime radicalC2×C3×C5×C11C4
cosocleC11×Dic5C2×C3
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 42);