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C₇⋊C₉×C₉₇ #20259167

order	6111
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₉×C₉₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇⋊C₉×C₉₇
unambiguous semidirect product	C₇⋊(C₉×C₉₇)

Splittings

derived, Sylow	C₇ ⋊ C₉×C₉₇
Hall	C₇×C₉₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₉₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₉₇
Frattini	C₃	ΓL(1,𝔽₈)×C₉₇
Fitting, socle	C₃×C₇×C₉₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₉₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1455 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇⋊C₉×C₉₇, C₇⋊C₉×D₉₇, C₉₇×D₇⋊C₉, …
maximal normal subgroup of	C₂×C₇⋊C₉×C₉₇, C₇⋊C₉×D₉₇, C₉₇×D₇⋊C₉, …
maximal quotient of	C₂×C₇⋊C₉×C₉₇, C₉₇×C₂²⋊(C₇⋊C₉), C₅×C₇⋊C₉×C₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6111, 2);