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#30636671

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

C₁₂₇ ⋊ #1323

Subgroups

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₂₇)⋊C₄
commutator	C₂×C₄×C₁₂₇	C₂×C₈
Frattini	C₂²×C₈	C₂×D₁₂₇
Fitting	C₂²⋊C₁₆×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²⋊C₈
prime radical	C₂³×C₁₂₇	M₁₆
cosocle	C₂²×C₈×C₁₂₇	C₂²
hypercenter	C₂²⋊C₁₆	D₁₂₇
hypocenter	C₁₂₇	#1323
LCS	G ▷ C₂×C₄×C₁₂₇ ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,127|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^126

Conjugacy classes & character table

2558 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2451);