#23766708

order	10112
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₇₉ ⋊ #2402

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Frattini	C₂³	C₂³×D₇₉
Fitting	C₄×C₄⋊C₄×C₇₉	C₂
hypercenter	C₄×C₄⋊C₄	D₇₉
hypocenter	C₇₉	#2402
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

400 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 161 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=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^78,c^b=cg,h^b=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, 7818);