Finite Group Databasebeta

← Prev (#44472576) Next (#44472578) →

C₂×D₇×C₁₇×C₇⋊C₉ #44472577

order	29988
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

C₂×D₇×C₁₇×C₇⋊C₉

Splittings

derived, Sylow	C₇² ⋊ C₂²×C₉×C₁₇
Hall	C₇×C₁₇×C₇⋊C₉ ⋊ C₂²
Hall	C₂×C₇×D₇×C₁₇ ⋊ C₉
Hall	C₇²×C₁₇ ⋊ C₂²×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₂²×C₁₇
Hall	C₂×C₇×D₇ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂²×C₉×C₁₇
Frattini	C₃	C₂×D₇×C₁₇×ΓL(1,𝔽₈)
Fitting, socle	C₂×C₃×C₇²×C₁₇	C₂×C₃
prime radical	C₂×C₃×C₇×D₇×C₁₇	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₇
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₇

128 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 4284

Conjugacy classes & character table

2550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 218);