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#30636600

order	16256
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₁₂₇ ⋊ #1290

Subgroups

	subgroup	G/H
center	C₂²	C₁₂₇⋊#95
commutator	C₂×C₄×C₁₂₇	C₄²
Frattini	C₂×C₄²	C₂×D₁₂₇
Fitting	C₂×C₄⋊C₈×C₁₂₇	C₂
socle	C₂²×C₁₂₇	#95
prime radical	C₂³×C₁₂₇	C₄⋊C₄
cosocle	C₂×C₄²×C₁₂₇	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₂₇
hypocenter	C₁₂₇	#1290
LCS	G ▷ C₂×C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,127|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^126,d^b=dg

Conjugacy classes & character table

2552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2380);