#23763553

order	10112
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₇₉ ⋊ #1843

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₇₉	C₂
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×C₄⋊C₈	D₇₉
hypocenter	C₇₉	#1843
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^78

1604 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 4663);