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C5×C11×C3⋊C8 #13050304

order1320
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C5×C8×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C3⋊C8
unambiguous semidirect productC3⋊(C5×C8×C11)

Splittings

derived, SylowC3 ⋊ C5×C8×C11
HallC3×C5×C11 ⋊ C8
HallC3×C11 ⋊ C5×C8
HallC3×C5 ⋊ C8×C11

Subgroups

subgroupG/H
center, hypercenterC4×C5×C11D3
commutator, hypocenterC3C5×C8×C11
FrattiniC4C5×D3×C11
FittingC3×C4×C5×C11C2
socle, prime radicalC2×C3×C5×C11C4
cosocleC3×C4C2×C5×C11
LCSG ▷ C3
UCSC1 ◁ C4×C5×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)(6,7,8,9,10,11,12,13,14,15,16)(18,19)(20,21,22,24,23,25,26,27);(17,18,19)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 8);