#23765307

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; only the 69 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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^b=h^78,h^c=h^78

1616 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 6417);