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C₂²×C₇×C₄₃⋊C₇ #22554596

order	8428
isoclinism	isoclinic class of C₄₃⋊C₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇² · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂²×C₇×C₄₃⋊C₇
unambiguous semidirect product	(C₂²×C₄₃)⋊C₇²
unambiguous semidirect product	(C₂²×C₇×C₄₃)⋊C₇

Splittings

Fitting, socle	C₂²×C₇×C₄₃ ⋊ C₇
derived, Sylow	C₄₃ ⋊ C₂²×C₇²
Hall	C₂²×C₄₃ ⋊ C₇²

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₇	C₄₃⋊C₇
commutator, hypocenter	C₄₃	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₄₃	C₇
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂²×C₇

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×C₂²⋊((C₄₃⋊C₃)⋊C₇), C₇×A₄×C₄₃⋊C₇, C₂²⋊(#11744749⋊C₇), …
maximal normal subgroup of	C₇×C₂²⋊((C₄₃⋊C₃)⋊C₇), C₇×A₄×C₄₃⋊C₇, C₂²⋊(#11744749⋊C₇), …
maximal quotient of	C₂×D₃×C₇×C₄₃⋊C₇, C₂²×C₃×C₇×C₄₃⋊C₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8428, 29);