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C37×C11⋊C5 #14523262

order2035
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×C11⋊C5
unambiguous semidirect productC11⋊(C5×C37)
unambiguous semidirect product(C11×C37)⋊C5

Splittings

Fitting, socle, HallC11×C37 ⋊ C5
derived, SylowC11 ⋊ C5×C37

Subgroups

subgroupG/H
center, hypercenterC37C11⋊C5
commutator, cosocle, hypocenterC11C5×C37
FrattiniC1G
Fitting, socleC11×C37C5
LCSG ▷ C11
UCSC1 ◁ C37

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 407

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(39,40,42,45,44)(41,43,47,48,46);(38,39,41,44,40,42,46,48,43,45,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C37×C11⋊C5, C11⋊C5×D37, C37×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C37×C11⋊C5, C11⋊C5×D37, C37×AGL(1,𝔽11), …
maximal quotient ofC2×C37×C11⋊C5, C7×C37×C11⋊C5, C37×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2035, 1);