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Q₈×C₁₂₇⋊C₁₆ #30640634

order	16256
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×C₁₂₇⋊C₁₆

Splittings

C₁₂₇ ⋊ Q₈×C₁₆

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₂₇
commutator	C₂×C₁₂₇	C₂²×C₁₆
Fitting	C₈×Q₈×C₁₂₇	C₂
socle, prime radical	C₂²×C₁₂₇	C₂²×C₈
cosocle	C₂×C₈×C₁₂₇	C₂³
hypercenter	C₈×Q₈	D₁₂₇
hypocenter	C₁₂₇	Q₈×C₁₆
LCS	G ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6414);