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C₄×Q₃₂×C₇₉ #23759796

order	10112
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Q₃₂×C₇₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₇₉	D₈
commutator	C₈	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₈	C₂³×C₇₉
socle, prime radical	C₂²×C₇₉	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ C₄²×C₇₉ ◁ C₄×C₈×C₇₉ ◁ G

150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3476 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₄×Q₃₂×D₇₉, C₄×#19098996, C₄×#19099005, …
maximal subgroup of	C₇₉×#7384, C₇₉×#7386, C₈×Q₃₂×C₇₉, …
maximal normal subgroup of	C₇₉×#7384, C₇₉×#7386, C₈×Q₃₂×C₇₉, …
maximal quotient of	C₈×Q₃₂×C₇₉, C₇₉×#12072, C₇₉×#12083, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 906);