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C3×C7×#1044 #14523633

order2100
isoclinismisoclinic class of #1044
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×#1044

Splittings

Fitting, socle, HallC3×C52×C7 ⋊ C4
derived, SylowC52 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4
HallC3×C52 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7#1044
commutator, hypocenterC52C3×C4×C7
FrattiniC1G
Fitting, socleC3×C52×C7C4
prime radicalC3×C7×C5⋊D5C2
cosocleC5⋊D5C2×C3×C7
LCSG ▷ C52
UCSC1 ◁ C3×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 210

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C49×#1044, C7×ΓL(1,𝔽8)⋊#1044, C7×ΓL(1,𝔽8)×#1044, …
maximal normal subgroup ofC3×C49×#1044, C3×C72×#1044, C3×C7×C11×#1044, …
maximal quotient ofC3×C49×#1044, C7×ΓL(1,𝔽8)⋊#1044, C7×ΓL(1,𝔽8)×#1044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 113);