C₇×D₂₁⋊(C₅⋊D₅) #28413535

order	14700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₇×D₂₁⋊(C₅⋊D₅)
unambiguous semidirect product	D₂₁⋊(C₇×C₅⋊D₅)

	subgroup	G/H
center, hypercenter	C₇	D₂₁⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₃×C₅²×C₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂²
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₇

416 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

1113 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 714);