C₂×C₃×C₂₅×C₈₉ #27211157

order	13350
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₃₅₀
abelian	C₂×C₃×C₂₅×C₈₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₃×C₅×C₈₉
socle, prime radical	C₂×C₃×C₅×C₈₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 13350

A minimal faithful permutation representation — 1 generator on 119 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)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119)

Conjugacy classes & character table

13350 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₃₅₀, D₂₆₇₀₀
Fitting subgroup of	C₃×C₂₅×Dic₈₉, C₃×C₈₉×Dic₂₅, C₃×Dic₂₂₂₅, …
maximal subgroup of	C₃×C₄×C₂₅×C₈₉, C₃×C₂₅×Dic₈₉, C₃×C₈₉×Dic₂₅, …
maximal normal subgroup of	C₃×C₄×C₂₅×C₈₉, C₃×C₂₅×Dic₈₉, C₃×C₈₉×Dic₂₅, …
maximal quotient of	C₃×C₄×C₂₅×C₈₉, C₂²×C₃×C₂₅×C₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13350, 1);

C2×C3×C25×C89 #27211157