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C11⋊C5×D39 #16864259

order4290
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D39
unambiguous semidirect productC3⋊(D13×C11⋊C5)
unambiguous semidirect productC13⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D39)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C13 ⋊ C2×C5
HallC3×C13×C11⋊C5 ⋊ C2
HallC11×D39 ⋊ C5
HallC13×C11⋊C5 ⋊ D3
HallC3×C11⋊C5 ⋊ D13
HallC11×C13 ⋊ C5×D3
HallC3×C13 ⋊ C2×C11⋊C5
HallC3×C11 ⋊ C5×D13
SylowC13 ⋊ D3×C11⋊C5
SylowC11 ⋊ C5×D39
SylowC3 ⋊ D13×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C13C2×C5
LCSG ▷ C3×C11×C13
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 429

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×D117, C11⋊C5×C3⋊(D13⋊C3), C3×C11⋊C5×D39, …
maximal normal subgroup ofC11⋊C5×C3⋊(D13⋊C3), C3×C11⋊C5×D39, C5×C11⋊C5×D39, …
maximal quotient ofC11⋊C5×D117, C3×C11⋊C5×D39, C11⋊C5×C3⋊D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 24);