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C52×C3⋊#261 #16839155

order3900
isoclinismisoclinic class of C3⋊#261
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊#261
unambiguous semidirect productC3⋊(C52×#261)

Splittings

Fitting, socle, HallC3×C52×C13 ⋊ C4
derived, HallC3×C13 ⋊ C4×C52
HallC52×C13 ⋊ Dic3
HallC3×C52 ⋊ #261
SylowC13 ⋊ C52×Dic3
SylowC3 ⋊ C52×#261

Subgroups

subgroupG/H
center, hypercenterC52C3⋊#261
commutator, hypocenterC3×C13C4×C52
FrattiniC1G
Fitting, socleC3×C52×C13C4
prime radicalC3×C52×D13C2
cosocleC3×D13C2×C52
LCSG ▷ C3×C13
UCSC1 ◁ C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 975

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC52×C9⋊#261, C52×C3⋊AGL(1,𝔽13), C3⋊(#261⋊(C52⋊C3)), …
maximal normal subgroup ofC52×C3⋊AGL(1,𝔽13), C3⋊(#261⋊(C52⋊C3)), C52⋊C3×C3⋊#261, …
maximal quotient ofC52×C9⋊#261, C3×C52×C3⋊#261, C52×C3⋊(C3⋊#261), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3900, 163);