#44400458

order	29056
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

C₂₂₇ ⋊ #1940

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₂₇
commutator, socle, prime radical	C₂³×C₂₂₇	C₂²×C₄
Fitting	C₄×C₄⋊C₄×C₂₂₇	C₂
cosocle	C₂²×C₄×C₂₂₇	C₂³
hypercenter	C₄×C₄⋊C₄	D₂₂₇
hypocenter	C₂₂₇	#1940
LCS	G ▷ C₂³×C₂₂₇ ▷ C₂₂₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

248 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

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

μ_t(G) = 29056

Polycyclic presentation:

2^7,227|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^226,c^b=cg,h^b=h^226

4564 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 5234);