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C₇×D₅₅₃ #21440972

order	7742
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₅₅₃
unambiguous semidirect product	C₇⋊(C₇×D₇₉)
unambiguous semidirect product	C₇₉⋊(C₇×D₇)

Splittings

Fitting, socle, Hall	C₇²×C₇₉ ⋊ C₂
derived	C₇×C₇₉ ⋊ C₂×C₇
Sylow	C₇₉ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₅₅₃
commutator, hypocenter	C₇×C₇₉	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₇₉	C₂
LCS	G ▷ C₇×C₇₉
UCS	C₁ ◁ C₇

22 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1946 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₇×D₇₉, D₇×D₅₅₃, (C₇⋊D₇)⋊D₇₉, …
maximal normal subgroup of	C₇×D₇×D₇₉, D₇×D₅₅₃, (C₇⋊D₇)⋊D₇₉, …
maximal quotient of	C₇×Dic₅₅₃, C₂×C₇×D₅₅₃, C₃×C₇×D₅₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7742, 8);