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C11⋊C5×#595 #16836670

order3740
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×#595
unambiguous semidirect product(C11×#595)⋊C5

Splittings

Fitting, socle, derived, HallC11×C17 ⋊ C4×C5
HallC17×C11⋊C5 ⋊ C4
HallC11×#595 ⋊ C5
SylowC17 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×#595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C17C4×C5
prime radicalD17×C11⋊C5C2
cosocleC11×D17C2×C5
LCSG ▷ C11×C17
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 187

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×#595, C11⋊C5×C3⋊#595, C5×C11⋊C5×#595, …
maximal normal subgroup ofC3×C11⋊C5×#595, C5×C11⋊C5×#595, C7×C11⋊C5×#595, …
maximal quotient ofC3×C11⋊C5×#595, C11⋊C5×C3⋊#595, #595×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 16);