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Cayley diagram

C2×C29⋊C7 #87958

order406
isoclinismisoclinic class of C29⋊C7
automorphismAut(G) = AGL(1,𝔽29) (order 812) · Inn(G) = C29⋊C7 · Out(G) = C4
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C29⋊C7
unambiguous semidirect product(C2×C29)⋊C7

Splittings

Fitting, socle, HallC2×C29 ⋊ C7
derived, SylowC29 ⋊ C2×C7

Subgroups

subgroupG/H
center, hypercenterC2C29⋊C7
commutator, cosocle, hypocenterC29C2×C7
FrattiniC1G
Fitting, socleC2×C29C7
LCSG ▷ C29
UCSC1 ◁ C2

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 58

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

22 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic29⋊C7, C4×C29⋊C7, C2×D29⋊C7, …
maximal normal subgroup ofDic29⋊C7, C4×C29⋊C7, C2×D29⋊C7, …
maximal quotient ofC4×C29⋊C7, C22×C29⋊C7, D3×C29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(406, 2);