C₄₃×C₇⋊C₉ #14582148

order	2709
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₉×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₃×C₇⋊C₉
unambiguous semidirect product	C₇⋊(C₉×C₄₃)

Splittings

derived, Sylow	C₇ ⋊ C₉×C₄₃
Hall	C₇×C₄₃ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₃	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₄₃
Frattini	C₃	ΓL(1,𝔽₈)×C₄₃
Fitting, socle, prime radical	C₃×C₇×C₄₃	C₃
cosocle	C₃×C₇	C₃×C₄₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 2709

A minimal faithful permutation representation — 2 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)(45,46,47)(48,50,49)(51,52,54,53,55,57,56,58,59);(44,45,46,48,47,49,50)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₃×C₂²⋊(C₇⋊C₉), C₅×C₄₃×C₇⋊C₉, C₄₃×C₄₉⋊C₉, …
maximal normal subgroup of	C₅×C₄₃×C₇⋊C₉, C₇⋊C₉×C₄₃⋊C₇, C₇×C₄₃×C₇⋊C₉, …
maximal quotient of	C₄₃×C₂²⋊(C₇⋊C₉), C₅×C₄₃×C₇⋊C₉, C₄₃×C₄₉⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2709, 4);

C43×C7⋊C9 #14582148