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ΓL(1,𝔽8)×#1181 #14578481

order2436
isoclinismisoclinic class of ΓL(1,𝔽8)×#1181
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×#1181
unambiguous semidirect product(C7×#1181)⋊C3

Splittings

Fitting, socle, derived, HallC7×C29 ⋊ C3×C4
HallC7×#1181 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C4
SylowC29 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×#1181

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C29C3×C4
prime radicalΓL(1,𝔽8)×D29C2
cosocleC7×D29C2×C3
LCSG ▷ C7×C29
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 203

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

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

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#1181×C49⋊C3, ΓL(1,𝔽8)×AGL(1,𝔽29), C7×ΓL(1,𝔽8)×#1181, …
maximal normal subgroup ofΓL(1,𝔽8)×AGL(1,𝔽29), C7×ΓL(1,𝔽8)×#1181, C11×ΓL(1,𝔽8)×#1181, …
maximal quotient of#1181×C49⋊C3, C7×ΓL(1,𝔽8)×#1181, #30684932, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2436, 27);