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C₅×C₉×D₇×C₁₇ #24924189

order	10710
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₉×D₇×C₁₇

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉×C₁₇	D₇
commutator, hypocenter	C₇	C₂×C₅×C₉×C₁₇
Frattini	C₃	C₃×C₅×D₇×C₁₇
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₇×C₁₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₅×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₉×C₁₇

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3825 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₇×D₁₇, C₉×D₅×D₇×C₁₇, C₉×D₇×D₈₅, …
maximal normal subgroup of	C₅×C₉×D₇×D₁₇, C₉×D₅×D₇×C₁₇, C₉×D₇×D₈₅, …
maximal quotient of	C₅×C₉×C₁₇×Dic₇, C₂×C₅×C₉×D₇×C₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 4);