C₄×C₉×C₁₃×C₆₇ #44535565

order	31356
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₃₅₆
abelian	C₄×C₉×C₁₃×C₆₇
multiplicative	(ℤ/31357)ˣ, (ℤ/62714)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₁₃×C₆₇
socle, prime radical	C₂×C₃×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 31356

A minimal faithful permutation representation — 1 generator on 93 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)

Conjugacy classes & character table

31356 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₆₇₈, D₃₁₃₅₆
maximal subgroup of	Dic₁₅₆₇₈, D₃₁₃₅₆
maximal normal subgroup of	Dic₁₅₆₇₈, D₃₁₃₅₆
automorphism group of	C₃₁₃₅₇
outer automorphism group of	C₃₁₃₅₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 1);

C4×C9×C13×C67 #44535565