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C₂×C₉×Dic₇ #92601

order	504
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×Dic₇

Splittings

derived, Sylow	C₇ ⋊ C₂×C₄×C₉
Hall	C₇×C₉ ⋊ C₂×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₉	D₇
commutator, hypocenter	C₇	C₂×C₄×C₉
Frattini	C₂×C₃	C₂×C₃×D₇
Fitting	C₂²×C₇×C₉	C₂
socle, prime radical	C₂²×C₃×C₇	C₂×C₃
cosocle	C₂×C₃×C₇	C₂²×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂²×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2)(3,4,5,6)(8,9)(10,11)(12,13)(14,21,20,16,15,22,19,18,17);(1,2)(7,8,10,12,13,11,9)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₇×Dic₉, #11758871, Dic₉⋊Dic₇, …
maximal normal subgroup of	Dic₇×Dic₉, #11758871, Dic₉⋊Dic₇, …
maximal quotient of	C₂×C₉×C₇⋊C₈, C₉×#1136, C₄×C₉×Dic₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 27);