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C3×C7×#1042 #14523635

order2100
isoclinismisoclinic class of #1042
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×#1042

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#1042
commutator, hypocenterC52C3×C4×C7
FrattiniC1G
Fitting, socleC3×C52×C7C4
prime radicalC3×C5×C7×D5C2
cosocleC5×D5C2×C3×C7
LCSG ▷ C52
UCSC1 ◁ C3×C7

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 420

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C49×#1042, C7×ΓL(1,𝔽8)⋊#1042, C7×ΓL(1,𝔽8)×#1042, …
maximal normal subgroup ofC3×C49×#1042, C3×C72×#1042, C3×C7×C11×#1042, …
maximal quotient ofC3×C49×#1042, C7×ΓL(1,𝔽8)⋊#1042, C7×ΓL(1,𝔽8)×#1042, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 115);