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C5×C11×#595 #16836675

order3740
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#595

Splittings

Fitting, socle, HallC5×C11×C17 ⋊ C4
derived, SylowC17 ⋊ C4×C5×C11
HallC11×C17 ⋊ C4×C5
HallC5×C17 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11#595
commutator, hypocenterC17C4×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C17C4
prime radicalC5×C11×D17C2
cosocleD17C2×C5×C11
LCSG ▷ C17
UCSC1 ◁ C5×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 935

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(18,19,20,22)(21,24,25,29)(23,28,26,27)(30,32,33,31);(17,18,21,26,22,27,31,33,29,24,30,32,28,19,23,25,20)

Conjugacy classes & character table

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

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 21);