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C3×C5×C11⋊C8 #13050301

order1320
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11⋊C8

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5D11
commutator, hypocenterC11C3×C5×C8
FrattiniC4C3×C5×D11
FittingC3×C4×C5×C11C2
socle, prime radicalC2×C3×C5×C11C4
cosocleC4×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C3×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)(4,5,6,7,8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,22,24,23,25,26,27);(9,10,12,14,16,18,19,17,15,13,11)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 5);