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C₂×C₅×(C₁₃⋊C₉)⋊D₁₃ #44477706

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×(C₁₃⋊C₉)⋊D₁₃
unambiguous semidirect product	(C₂×C₁₃⋊C₉)⋊(C₅×D₁₃)

Splittings

derived, Sylow	C₁₃² ⋊ C₂²×C₅×C₉
Hall	C₅×C₁₃×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×C₅×C₁₃⋊D₁₃ ⋊ C₉
Hall	C₁₃×C₁₃⋊C₉ ⋊ C₂²×C₅
Hall	C₅×C₁₃² ⋊ C₂²×C₉
Hall	C₂×C₁₃⋊D₁₃ ⋊ C₅×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	(C₁₃⋊C₃)⋊D₁₃
commutator, hypocenter	C₁₃²	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×(C₁₃⋊C₃)⋊D₁₃
Fitting, socle	C₂×C₃×C₅×C₁₃²	C₂×C₃
prime radical	C₂×C₃×C₅×C₁₃⋊D₁₃	C₃
cosocle	C₃×C₁₃²	C₂²×C₃×C₅
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₂×C₃×C₅

200 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 1170

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 295);