Finite Group Databasebeta

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Q₃₂×C₄₃⋊C₈ #25008331

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

Q₃₂×C₄₃⋊C₈

Splittings

C₄₃ ⋊ C₈×Q₃₂

Subgroups

	subgroup	G/H
center	C₂×C₄	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄×Q₃₂×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₄×D₈
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	C₄×Q₃₂	D₄₃
hypocenter	C₄₃	C₈×Q₃₂
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₃₂

226 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 81302);