C₂×C₃×C₅×C₂₃×C₃₇ #38784273

order	25530
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₅₅₃₀
abelian	C₂×C₃×C₅×C₂₃×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 25530

A minimal faithful permutation representation — 1 generator on 70 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)

Conjugacy classes & character table

25530 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₇₆₅, C₂×D₁₂₇₆₅
socle of	Dic₁₂₇₆₅, C₂×D₁₂₇₆₅
maximal subgroup of	Dic₁₂₇₆₅, C₂×D₁₂₇₆₅
maximal normal subgroup of	Dic₁₂₇₆₅, C₂×D₁₂₇₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25530, 1);

C2×C3×C5×C23×C37 #38784273