#34296607

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1832	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1832	D₇₉
hypocenter	C₇₉	#21676
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1832

658 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 239 normal subgroups are shown.

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

μ_t(G) = 20224

Polycyclic presentation:

2^8,79|a^2=g,b^2=f,c^2=e,d^2=eg,g^2=h,b^a=be,c^a=cf,c^b=ch,i^d=i^78

1804 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 177906);