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C₂×C₁₉×#11725075 #45691634

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₁₉×#11725075

Splittings

derived, Sylow	C₇² ⋊ C₂²×C₉×C₁₉
Hall	C₁₉×#89205 ⋊ C₂²
Hall	C₂×C₇×D₇×C₁₉ ⋊ C₉
Hall	C₇²×C₁₉ ⋊ C₂²×C₉
Hall	#89205 ⋊ C₂²×C₁₉
Hall	C₂×C₇×D₇ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	#64422
commutator, hypocenter	C₇²	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×#64422
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₇×D₇×C₁₉	C₃
cosocle	C₃×C₇²	C₂²×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₉

128 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 4788

Conjugacy classes & character table

1938 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 432);