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C₉×C₁₁×D₇ #13063451

order	1386
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₁×D₇

Splittings

Fitting, Hall	C₇×C₉×C₁₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₁
Hall	C₇×C₁₁ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₁	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₁
Frattini	C₃	C₃×C₁₁×D₇
Fitting	C₇×C₉×C₁₁	C₂
socle	C₃×C₇×C₁₁	C₂×C₃
prime radical	C₃×C₁₁×D₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 693

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27);(22,27)(23,26)(24,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×D₇×D₁₁, C₁₁×D₇×D₉, D₇×D₉₉, …
maximal normal subgroup of	C₉×D₇×D₁₁, C₁₁×D₇×D₉, D₇×D₉₉, …
maximal quotient of	C₉×C₁₁×Dic₇, C₂×C₉×C₁₁×D₇, C₉×D₇×C₁₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1386, 6);