Finite Group Databasebeta

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C₄⋊C₈×C₄₇⋊C₈ #26107401

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂×C₈² · Schur multiplier (H₂) = C₂²×C₈

Aliases

C₄⋊C₈×C₄₇⋊C₈

Splittings

C₄₇ ⋊ C₈×C₄⋊C₈

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₈²
Fitting	C₄×C₄⋊C₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₄²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₈×C₄⋊C₈
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₄⋊C₈

550 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60691);