Finite Group Databasebeta

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C2×C3×C17⋊#64424 #44472877

order29988
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C17⋊#64424
unambiguous semidirect product(C2×C17)⋊(C3×#64424)

Splittings

Fitting, socleC2×C3×C72×C17 ⋊ C2×C3
derived, HallC72×C17 ⋊ C22×C32
HallC3×C17×#3861 ⋊ C22
HallC2×C7⋊D119 ⋊ C32
HallC3×#3861 ⋊ C2×D17
SylowC72 ⋊ C2×C32×D17
SylowC17 ⋊ C2×C3×#64424

Subgroups

subgroupG/H
center, hypercenterC2×C3C17⋊#64424
commutator, cosocle, hypocenterC72×C17C22×C32
FrattiniC1G
Fitting, socleC2×C3×C72×C17C2×C3
LCSG ▷ C72×C17
UCSC1 ◁ C2×C3

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 4998

A minimal faithful permutation representation — 3 generators on 36 points:

(7,10,11,8,9,12)(14,17,18,15,16,19)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);(1,2)(3,4,5)(13,14,16,19,18,17,15)(20,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22);(6,7,9,12,11,10,8)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 518);