C₂×C₇×C₃₇×C₅₃ #42117186

order	27454
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₇₄₅₄
abelian	C₂×C₇×C₃₇×C₅₃

Subgroups

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

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 99
transitive degree	μ_t(G) = 27454

A minimal faithful permutation representation — 1 generator on 99 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)

Conjugacy classes & character table

27454 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₃₇₂₇, C₂×D₁₃₇₂₇
socle of	Dic₁₃₇₂₇, C₂×D₁₃₇₂₇
maximal subgroup of	Dic₁₃₇₂₇, C₂×D₁₃₇₂₇
maximal normal subgroup of	Dic₁₃₇₂₇, C₂×D₁₃₇₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27454, 1);

C2×C7×C37×C53 #42117186