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C11×C17×Dic5 #16836663

order3740
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×Dic5

Splittings

derived, SylowC5 ⋊ C4×C11×C17
HallC5×C11×C17 ⋊ C4
HallC5×C17 ⋊ C4×C11
HallC5×C11 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D5
commutator, hypocenterC5C4×C11×C17
FrattiniC2D5×C11×C17
Fitting, socle, prime radicalC2×C5×C11×C17C2
cosocleC2×C5C2×C11×C17
LCSG ▷ C5
UCSC1 ◁ C2×C11×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 3740

A minimal faithful permutation representation — 2 generators on 37 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);(29,31,30,32)(34,37)(35,36)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×C17×Dic5, C11×C17×Dic15, C11×C17×Dic25, …
maximal normal subgroup ofC3×C11×C17×Dic5, C17×Dic5×C11⋊C5, C5×C11×C17×Dic5, …
maximal quotient ofC3×C11×C17×Dic5, C11×C17×Dic15, C11×C17×Dic25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 9);