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C₇×D₇×C₇₉ #21440971

order	7742
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₇×C₇₉
unambiguous semidirect product	C₇⋊(C₂×C₇×C₇₉)

Splittings

Fitting, socle, Hall	C₇²×C₇₉ ⋊ C₂
derived	C₇ ⋊ C₂×C₇×C₇₉
Sylow	C₇² ⋊ C₂×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₇₉	D₇
commutator, hypocenter	C₇	C₂×C₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₇²×C₇₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₇×C₇₉

22 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2765 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₇×D₇₉, D₇²×C₇₉, D₇×D₅₅₃, …
maximal normal subgroup of	C₇×D₇×D₇₉, D₇²×C₇₉, D₇×D₅₅₃, …
maximal quotient of	C₇×Dic₇×C₇₉, C₂×C₇×D₇×C₇₉, C₃×C₇×D₇×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7742, 7);