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C3×#63242 #11717837

order816
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2

Aliases

direct productC3×#63242

Splittings

derived, SylowC17 ⋊ C2×C3×C8
HallC3×C17 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC3×C4#595
commutator, hypocenterC17C2×C3×C8
FrattiniC2C2×C3×#595
FittingC3×C4×C17C4
socleC2×C3×C17C2×C4
prime radicalC2×C3×D17C4
cosocleDic17C22×C3
LCSG ▷ C17
UCSC1 ◁ C3×C4

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13108885, #13108887, #13108889, …
maximal normal subgroup of#13108885, #13108887, #13108889, …
maximal quotient ofC3×#10587529, C3×#10587530, C3×C4×#3624, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(816, 107);