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C3×C7×#1035 #14523540

order2100
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×#1035

Splittings

Fitting, HallC3×C7×C25 ⋊ C4
derived, SylowC25 ⋊ C3×C4×C7
HallC7×C25 ⋊ C3×C4
HallC3×C25 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7#1035
commutator, hypocenterC25C3×C4×C7
FrattiniC5C3×C7×AGL(1,𝔽5)
FittingC3×C7×C25C4
socleC3×C5×C7AGL(1,𝔽5)
prime radicalC3×C7×D25C2
cosocleD25C2×C3×C7
LCSG ▷ C25
UCSC1 ◁ C3×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 525

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C49×#1035, C7×ΓL(1,𝔽8)⋊#1035, C7×ΓL(1,𝔽8)×#1035, …
maximal normal subgroup ofC3×C49×#1035, C3×C72×#1035, C3×C7×C11×#1035, …
maximal quotient ofC3×C49×#1035, C7×ΓL(1,𝔽8)⋊#1035, C7×ΓL(1,𝔽8)×#1035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 20);