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C11⋊C5×C67 #16814767

order3685
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C67 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×C67
unambiguous semidirect productC11⋊(C5×C67)
unambiguous semidirect product(C11×C67)⋊C5

Splittings

Fitting, socle, HallC11×C67 ⋊ C5
derived, SylowC11 ⋊ C5×C67

Subgroups

subgroupG/H
center, hypercenterC67C11⋊C5
commutator, cosocle, hypocenterC11C5×C67
FrattiniC1G
Fitting, socleC11×C67C5
LCSG ▷ C11
UCSC1 ◁ C67

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 78
transitive degreeμt(G) = 737

A minimal faithful permutation representation — 2 generators on 78 points:

(2,3,5,8,7)(4,6,10,11,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78);(1,2,4,7,3,5,9,11,6,8,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C11⋊C5×C67, C11⋊C5×C67⋊C3, C5×C11⋊C5×C67, …
maximal normal subgroup ofC3×C11⋊C5×C67, C11⋊C5×C67⋊C3, C5×C11⋊C5×C67, …
maximal quotient ofC3×C11⋊C5×C67, C67×C11⋊C25, C5×C11⋊C5×C67, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3685, 2);