#37555771

order	23571
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

C₉₇ ⋊ #6858

	subgroup	G/H
center	C₃²	C₃²⋊(C₉₇⋊C₃)
commutator, prime radical, cosocle	C₃³×C₉₇	C₃²
Frattini	C₃³	C₃×C₉₇⋊C₃
Fitting	C₃²⋊C₉×C₉₇	C₃
socle	C₃²×C₉₇	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₉₇⋊C₃
hypocenter	C₉₇	#6858
LCS	G ▷ C₃³×C₉₇ ▷ C₃²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

60 conjugacy classes of subgroups.

μ_t(G) = 7857

Polycyclic presentation:

3^5,97|a^3=d,b^3=d,b^a=bc,c^a=cd,f^a=f^61,c^b=ce,f^b=f^35

1091 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 78);