C₅×C₁₃⋊C₂₇ #13182168

order	1755
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₅×C₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₃⋊C₂₇
unambiguous semidirect product	C₁₃⋊(C₅×C₂₇)
unambiguous semidirect product	(C₅×C₁₃)⋊C₂₇

Splittings

derived, Sylow	C₁₃ ⋊ C₅×C₂₇
Hall	C₅×C₁₃ ⋊ C₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₅×C₂₇
Frattini	C₉	C₅×C₁₃⋊C₃
Fitting	C₅×C₉×C₁₃	C₃
socle, prime radical	C₃×C₅×C₁₃	C₉
cosocle	C₉×C₁₃	C₃×C₅
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1755

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3,4,5)(7,8,10)(9,12,15)(11,14,13)(16,18,17)(19,20,23,21,24,29,26,31,36,22,25,30,27,32,37,34,39,42,28,33,38,35,40,43,41,44,45);(6,7,9,8,11,15,12,16,18,10,13,17,14)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1755, 1);

C5×C13⋊C27 #13182168