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C3×C5×Dic14 #11719794

order840
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic14

Splittings

HallC3×C5×C7 ⋊ Q8
HallC5×C7 ⋊ C3×Q8
HallC3×C7 ⋊ C5×Q8
SylowC7 ⋊ C3×C5×Q8

Subgroups

subgroupG/H
centerC2×C3×C5C2×D7
commutator, cosocleC2×C7C22×C3×C5
FrattiniC2C2×C3×C5×D7
FittingC3×C4×C5×C7C2
socle, prime radicalC2×C3×C5×C7C22
hypercenterC3×C4×C5D7
hypocenterC7C3×C5×Q8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3×C5 ◁ C3×C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 840

A minimal faithful permutation representation — 2 generators on 23 points:

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10587845, C3×#10587847, C3×#10587850, …
maximal normal subgroup ofC3×#10587845, C3×#10587847, C3×#10587850, …
maximal quotient ofC3×C5×Dic7⋊C4, C3×C5×C4⋊Dic7, C2×C3×C5×Dic14

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(840, 96);