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C₉×D₇×D₇₇ #34084703

order	19404
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₇×D₇₇

Splittings

Fitting, Hall	C₇²×C₉×C₁₁ ⋊ C₂²
derived, Hall	C₇²×C₁₁ ⋊ C₂²×C₉
Hall	C₇²×C₉ ⋊ C₂×D₁₁
Hall	C₉×C₁₁ ⋊ D₇²
Sylow	C₇² ⋊ C₂×C₉×D₁₁
Sylow	C₁₁ ⋊ C₉×D₇²

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×D₇₇
commutator, hypocenter	C₇²×C₁₁	C₂²×C₉
Frattini	C₃	C₃×D₇×D₇₇
Fitting	C₇²×C₉×C₁₁	C₂²
socle, cosocle	C₃×C₇²×C₁₁	C₂²×C₃
prime radical	C₃×D₇×D₇₇	C₃
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₉

156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1386

Conjugacy classes & character table

1800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 194);