#23765308

order	10112
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₇₉ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₉
commutator, socle, prime radical	C₂²×C₇₉	C₂²×C₈
Fitting	C₄×C₁₆×C₇₉	C₂
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2183
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

126 conjugacy classes of subgroups.

Polycyclic presentation:

2^7,79|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^78

2552 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 6418);