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AGL(1,𝔽5)×C29⋊C7 #16861024

order4060
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C29⋊C7
unambiguous semidirect product(AGL(1,𝔽5)×C29)⋊C7

Splittings

Fitting, socle, derived, HallC5×C29 ⋊ C4×C7
HallC5×C29⋊C7 ⋊ C4
HallAGL(1,𝔽5)×C29 ⋊ C7
SylowC29 ⋊ C7×AGL(1,𝔽5)
SylowC5 ⋊ C4×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C29C4×C7
prime radicalD5×C29⋊C7C2
cosocleD5×C29C2×C7
LCSG ▷ C5×C29
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 145

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#1035×C29⋊C7, C5×AGL(1,𝔽5)×C29⋊C7, #1042×C29⋊C7, …
maximal normal subgroup ofC5×AGL(1,𝔽5)×C29⋊C7, C7×AGL(1,𝔽5)×C29⋊C7, AGL(1,𝔽5)×D29⋊C7, …
maximal quotient of#1035×C29⋊C7, C5×AGL(1,𝔽5)×C29⋊C7, #1042×C29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4060, 18);