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C17×#1181 #14520305

order1972
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×#1181

Splittings

Fitting, socle, HallC17×C29 ⋊ C4
derived, SylowC29 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC17#1181
commutator, hypocenterC29C4×C17
FrattiniC1G
Fitting, socleC17×C29C4
prime radicalC17×D29C2
cosocleD29C2×C17
LCSG ▷ C29
UCSC1 ◁ C17

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 493

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20,21,23)(22,25,26,32)(24,29,30,28)(27,34,35,42)(31,38,39,40)(33,41,36,37)(43,45,46,44);(18,19,22,27,36,32,40,34,43,45,41,29,20,24,31,39,30,23,28,37,44,46,42,38,25,33,35,26,21)

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×AGL(1,𝔽29), C7×C17×#1181, C17×C7⋊#1181, …
maximal normal subgroup ofC17×AGL(1,𝔽29), C7×C17×#1181, C11×C17×#1181, …
maximal quotient ofC7×C17×#1181, C17×C7⋊#1181, C17×#11760329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1972, 5);