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C23×C29⋊C7 #17988028

order4669
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C29⋊C7
unambiguous semidirect productC29⋊(C7×C23)
unambiguous semidirect product(C23×C29)⋊C7

Splittings

Fitting, socle, HallC23×C29 ⋊ C7
derived, SylowC29 ⋊ C7×C23

Subgroups

subgroupG/H
center, hypercenterC23C29⋊C7
commutator, cosocle, hypocenterC29C7×C23
FrattiniC1G
Fitting, socleC23×C29C7
LCSG ▷ C29
UCSC1 ◁ C23

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 667

A minimal faithful permutation representation — 2 generators on 52 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26,28,31,32,38,43)(27,30,35,42,50,29,33)(34,41,39,47,51,37,40)(36,44,46,49,48,45,52);(24,25,27,30,36,45,44,31,37,46,47,33,40,48,42,51,26,29,34,35,43,50,52,38,28,32,39,41,49)

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C23×C29⋊C7, C5×C23×C29⋊C7, C7×C23×C29⋊C7
maximal normal subgroup ofC3×C23×C29⋊C7, C5×C23×C29⋊C7, C7×C23×C29⋊C7
maximal quotient ofC3×C23×C29⋊C7, C5×C23×C29⋊C7, C23×C29⋊C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4669, 1);