C₂×C₅×C₇×C₁₇×C₂₃ #41032837

order	27370
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₇₃₇₀
abelian	C₂×C₅×C₇×C₁₇×C₂₃

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) = 54
transitive degree	μ_t(G) = 27370

A minimal faithful permutation representation — 1 generator on 54 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)

Conjugacy classes & character table

27370 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₆₈₅, C₂×D₁₃₆₈₅
socle of	Dic₁₃₆₈₅, C₂×D₁₃₆₈₅
maximal subgroup of	Dic₁₃₆₈₅, C₂×D₁₃₆₈₅
maximal normal subgroup of	Dic₁₃₆₈₅, C₂×D₁₃₆₈₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27370, 1);

C2×C5×C7×C17×C23 #41032837