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C22×C3×C29⋊C7 #14578482

order2436
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C29⋊C7
unambiguous semidirect product(C22×C3×C29)⋊C7

Splittings

Fitting, socle, HallC22×C3×C29 ⋊ C7
derived, SylowC29 ⋊ C22×C3×C7
HallC22×C29 ⋊ C3×C7
HallC3×C29 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC22×C3C29⋊C7
commutator, cosocle, hypocenterC29C22×C3×C7
FrattiniC1G
Fitting, socleC22×C3×C29C7
LCSG ▷ C29
UCSC1 ◁ C22×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 348

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2)(5,6,7)(9,10,12,15,16,22,27)(11,14,19,26,34,13,17)(18,25,23,31,35,21,24)(20,28,30,33,32,29,36);(3,4)(8,9,11,14,20,29,28,15,21,30,31,17,24,32,26,35,10,13,18,19,27,34,36,22,12,16,23,25,33)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽7)×C29⋊C7, C22×ΓL(1,𝔽8)×C29⋊C7, C2×C3×D7×C29⋊C7, …
maximal normal subgroup ofC22×C3×C7×C29⋊C7, C22×C3×C11×C29⋊C7, C22×C3×C13×C29⋊C7, …
maximal quotient ofC22×C3×C29⋊C49, C2×AGL(1,𝔽7)×C29⋊C7, C22×ΓL(1,𝔽8)×C29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2436, 28);