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#30758154

order	17152
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₆₇ ⋊ #10232

Subgroups

	subgroup	G/H
center	C₂³	#14524013
commutator, cosocle	C₂×C₄²×C₆₇	C₂³
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×D₄⋊C₈×C₆₇	C₂
socle	C₂³×C₆₇	#120
prime radical	C₂²×D₄×C₆₇	D₄
hypercenter	C₂×D₄⋊C₈	D₆₇
hypocenter	C₆₇	#10232
LCS	G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×D₄⋊C₈

644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8576

Polycyclic presentation:

2^8,67|a^2=g,c^2=h,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^66,c^b=cf,d^b=dg,e^c=eh,i^c=i^66

Conjugacy classes & character table

1894 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 71891);