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#30636688

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

Aliases

No aliases for this group.

Splittings

C₁₂₇ ⋊ #1330

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₂₇
commutator	C₂×C₄×C₁₂₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₂₇
Fitting	#436×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²⋊C₈
prime radical	C₂×D₄×C₁₂₇	C₈
cosocle	C₄×C₈×C₁₂₇	C₂²
hypercenter	#436	D₁₂₇
hypocenter	C₁₂₇	#1330
LCS	G ▷ C₂×C₄×C₁₂₇ ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #436

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,127|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^126,c^b=ceg,d^b=dg

Conjugacy classes & character table

1802 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 2468);