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M₁₆×#10587739 #22578363

order	8768
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

M₁₆×#10587739

Splittings

Fitting	M₁₆×C₁₃₇ ⋊ C₄
Sylow	C₁₃₇ ⋊ C₄×M₁₆

Subgroups

	subgroup	G/H
center, Frattini	C₄	C₂²×#10587739
commutator, socle	C₂×C₁₃₇	C₂×C₄²
Fitting	M₁₆×C₁₃₇	C₄
hypercenter	M₁₆	#10587739
hypocenter	C₁₃₇	C₄×M₁₆
LCS	G ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₄ ◁ M₁₆

142 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#100×#10587739, #101×#10587739, #104×#10587739, …
maximal normal subgroup of	#100×#10587739, #101×#10587739, #104×#10587739, …
maximal quotient of	M₁₆×#11764047, #31795987, #31795990, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1509);