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C47⋊#64424 #28352474

order13818
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC47⋊#64424

Splittings

Fitting, socle, derived, HallC72×C47 ⋊ C2×C3
HallC47×#3861 ⋊ C2
HallC7⋊D329 ⋊ C3
Hall#3861 ⋊ D47
SylowC72 ⋊ C3×D47
SylowC47 ⋊ #64424

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C47C2×C3
LCSG ▷ C72×C47
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 2303

A minimal faithful permutation representation — 3 generators on 61 points:

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

Polycyclic presentation:

2,3,7^2,47|c^a=c^6,d^a=d^6,e^a=e^46,c^b=c^2,d^b=d^2

Conjugacy classes & character table

451 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD47×#64424, #64423⋊D47, C2×C47⋊#64424
maximal normal subgroup ofD47×#64424, #64423⋊D47, C2×C47⋊#64424
maximal quotient ofC47⋊#10596874, C2×C47⋊#64424

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13818, 18);