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C3×D5×C11×C13 #16864243

order4290
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C11×C13
unambiguous semidirect productC5⋊(C2×C3×C11×C13)

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C11×C13
HallC5×C11×C13 ⋊ C2×C3
HallC3×C5×C13 ⋊ C2×C11
HallC3×C5×C11 ⋊ C2×C13
HallC5×C13 ⋊ C2×C3×C11
HallC5×C11 ⋊ C2×C3×C13
HallC3×C5 ⋊ C2×C11×C13

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13D5
commutator, cosocle, hypocenterC5C2×C3×C11×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C2
LCSG ▷ C5
UCSC1 ◁ C3×C11×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 2145

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32);(5,8)(6,7)

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×D5×C11×C13, D5×C11×C13⋊C9, C3×D5×C11×C13⋊C3, …
maximal normal subgroup ofC9×D5×C11×C13, D5×C11×C13⋊C9, C3×D5×C11×C13⋊C3, …
maximal quotient ofC9×D5×C11×C13, C3×C11×C13×D15, C32×D5×C11×C13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 8);