C₂×C₁₇×C₁₉×C₂₅ #30633363

order	16150
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₁₅₀
abelian	C₂×C₁₇×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₅×C₁₇×C₁₉
socle, prime radical	C₂×C₅×C₁₇×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 16150

A minimal faithful permutation representation — 1 generator on 63 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)

Conjugacy classes & character table

16150 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₁₅₀, D₃₂₃₀₀
Fitting subgroup of	C₁₇×C₂₅×Dic₁₉, C₁₉×C₂₅×Dic₁₇, C₂₅×Dic₃₂₃, …
maximal subgroup of	C₄×C₁₇×C₁₉×C₂₅, C₁₇×C₂₅×Dic₁₉, C₁₉×C₂₅×Dic₁₇, …
maximal normal subgroup of	C₄×C₁₇×C₁₉×C₂₅, C₁₇×C₂₅×Dic₁₉, C₁₉×C₂₅×Dic₁₇, …
maximal quotient of	C₄×C₁₇×C₁₉×C₂₅, C₂²×C₁₇×C₁₉×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16150, 1);

C2×C17×C19×C25 #30633363