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C3×Dic47 #10588014

order564
isoclinismisoclinic class of D47
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic47
unambiguous semidirect productC47⋊(C3×C4)

Splittings

derived, SylowC47 ⋊ C3×C4
HallC3×C47 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2×C3D47
commutator, hypocenterC47C3×C4
FrattiniC2C3×D47
Fitting, socle, prime radicalC2×C3×C47C2
cosocleC2×C47C2×C3
LCSG ▷ C47
UCSC1 ◁ C2×C3

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 564

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2,3)(4,5)(6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(4,6,5,7)(9,54)(10,53)(11,52)(12,51)(13,50)(14,49)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×Dic47, D141⋊C4, #11765529, …
maximal normal subgroup ofD3×Dic47, D141⋊C4, #11765529, …
maximal quotient ofC3×C47⋊C8, C2×C3×Dic47, C9×Dic47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(564, 2);