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D5×C11×C13 #13083647

order1430
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×C13
unambiguous semidirect productC5⋊(C2×C11×C13)

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C2
derived, SylowC5 ⋊ C2×C11×C13
HallC5×C13 ⋊ C2×C11
HallC5×C11 ⋊ C2×C13

Subgroups

subgroupG/H
center, hypercenterC11×C13D5
commutator, cosocle, hypocenterC5C2×C11×C13
FrattiniC1G
Fitting, socleC5×C11×C13C2
LCSG ▷ C5
UCSC1 ◁ C11×C13

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 715

A minimal faithful permutation representation — 2 generators on 29 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);(2,5)(3,4)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×C13×AGL(1,𝔽5), C11×#63120, C13×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC11×C13×AGL(1,𝔽5), C11×#63120, C13×C11⋊AGL(1,𝔽5), …
maximal quotient ofC11×C13×Dic5, C2×D5×C11×C13, C3×D5×C11×C13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1430, 8);