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C5×C3⋊(C11⋊C8) #13050305

order1320
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C5×C8 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, HallC3×C11 ⋊ C5×C8
HallC3×C5×C11 ⋊ C8
HallC5×C11 ⋊ C3⋊C8
HallC3×C5 ⋊ C11⋊C8
SylowC11 ⋊ C5×C3⋊C8
SylowC3 ⋊ C5×C11⋊C8

Subgroups

subgroupG/H
center, hypercenterC4×C5D33
commutator, hypocenterC3×C11C5×C8
FrattiniC4C5×D33
FittingC3×C4×C5×C11C2
socle, prime radicalC2×C3×C5×C11C4
cosocleC3×C4×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C4×C5

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 9);