#34316402

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂×C₄	#14579130
commutator, prime radical, cosocle	C₂⁴×C₇₉	C₂⁴
Frattini	C₂⁴	C₂³×D₇₉
Fitting	C₇₉×#3458	C₂
socle	C₂²×C₇₉	C₂×#120
hypercenter	#3458	D₇₉
hypocenter	C₇₉	#23564
LCS	G ▷ C₂⁴×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3458

1162 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.

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

μ_t(G) = 5056

Polycyclic presentation:

2^8,79|a^2=e,b^2=e,c^2=e,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^c=i^78

1768 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 197701);