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C11×#1200 #13050364

order1320
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#1200

Splittings

derived, HallC3×C5 ⋊ C2×C4×C11
HallC3×C5×C11 ⋊ C2×C4
HallC5×C11 ⋊ C4×D3
HallC3×C11 ⋊ C4×D5
SylowC5 ⋊ C4×D3×C11
SylowC3 ⋊ C4×D5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×D5
commutator, hypocenterC3×C5C2×C4×C11
FrattiniC2D3×D5×C11
Fitting, socleC2×C3×C5×C11C22
prime radicalC2×C11×D15C2
cosocleC2×C3×C5C22×C11
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 660

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(18,19)(20,22,23,21);(13,14)(15,16)(17,18,19)(20,21,23,22)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 68);