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C3×C11×Dic10 #13050396

order1320
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic10
unambiguous semidirect productC5⋊(C3×Q8×C11)

Splittings

HallC3×C5×C11 ⋊ Q8
HallC5×C11 ⋊ C3×Q8
HallC3×C5 ⋊ Q8×C11
SylowC5 ⋊ C3×Q8×C11

Subgroups

subgroupG/H
centerC2×C3×C11C2×D5
commutator, cosocleC2×C5C22×C3×C11
FrattiniC2C2×C3×D5×C11
FittingC3×C4×C5×C11C2
socle, prime radicalC2×C3×C5×C11C22
hypercenterC3×C4×C11D5
hypocenterC5C3×Q8×C11
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C11 ◁ C3×C4×C11

48 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)(15,16,17,18)(19,22,21,20)(23,24,25,26,27);(15,19,17,21)(16,20,18,22)(24,27)(25,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 100);