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C17×C31⋊C3 #13096828

order1581
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C31⋊C3
unambiguous semidirect productC31⋊(C3×C17)
unambiguous semidirect product(C17×C31)⋊C3

Splittings

Fitting, socle, HallC17×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC17C31⋊C3
commutator, cosocle, hypocenterC31C3×C17
FrattiniC1G
Fitting, socleC17×C31C3
LCSG ▷ C31
UCSC1 ◁ C17

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 527

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)(19,20,22)(21,24,29)(23,27,26)(25,31,38)(28,34,36)(30,32,33)(35,41,45)(37,42,43)(39,46,40)(44,47,48);(18,19,21,25,32,22,26,33,40,46,29,36,43,31,39,38,45,48,41,24,30,37,44,47,34,20,23,28,35,42,27)

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C17×C31⋊C3, C17×D31⋊C3, D17×C31⋊C3, …
maximal normal subgroup ofC2×C17×C31⋊C3, C17×D31⋊C3, D17×C31⋊C3, …
maximal quotient ofC2×C17×C31⋊C3, C17×C31⋊C9, C3×C17×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1581, 1);