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C4×C49⋊C9 #13183482

order1764
isoclinismisoclinic class of C49⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C49⋊C9
unambiguous semidirect product(C4×C49)⋊C9

Splittings

derived, SylowC49 ⋊ C4×C9
HallC4×C49 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C4C49⋊C3
commutator, hypocenterC49C4×C9
Frattini, socle, prime radicalC2×C3×C7C2×ΓL(1,𝔽8)
FittingC3×C4×C49C3
cosocleC2×C3×C49C2×C3
LCSG ▷ C49
UCSC1 ◁ C3×C4

27 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 1764

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,3,4)(6,8,12)(7,11,19)(9,15,27)(10,17,24)(13,23,21)(14,26,35)(16,30,48)(18,34,22)(20,37,36)(25,42,41)(28,44,38)(29,47,33)(31,49,51)(32,45,39)(40,43,50)(46,53,52)(54,55,57,56,58,60,59,61,62);(5,49,34,44,29,28,52,11,10,9,53,22,21,30,19,27,14,13,31,43,23,37,47,33,32,15,41,42,7,6,51,50,12,46,45,20,18,8,16,26,39,38,36,35,17,25,24,48,40)

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic11×C49⋊C9, C4×C11×C49⋊C9, Dic13×C49⋊C9, …
maximal normal subgroup ofC4×C11×C49⋊C9, C4×C13×C49⋊C9, C4×C17×C49⋊C9, …
maximal quotient ofDic11×C49⋊C9, C4×C11×C49⋊C9, Dic13×C49⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1764, 2);