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D₄₇×D₄⋊C₁₆ #26125975

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂⁴

Aliases

D₄₇×D₄⋊C₁₆

Splittings

Fitting	C₄₇×D₄⋊C₁₆ ⋊ C₂
Sylow	C₄₇ ⋊ C₂×D₄⋊C₁₆

Subgroups

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₄₇
Fitting	C₄₇×D₄⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₈
prime radical	C₂×D₄×D₄₇	C₈
cosocle	C₄×C₈×C₄₇	C₂³
hypercenter	D₄⋊C₁₆	D₄₇
hypocenter	C₄₇	C₂×D₄⋊C₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ D₄⋊C₁₆

470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 79265);