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C₂×D₇⋊(C₁₁²⋊C₉) #44478943

order	30492
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₁₁

Aliases

direct product	C₂×D₇⋊(C₁₁²⋊C₉)
unambiguous semidirect product	D₇⋊(C₂×C₁₁²⋊C₉)
unambiguous semidirect product	(C₂×D₇)⋊(C₁₁²⋊C₉)

Splittings

derived, Hall	C₇×C₁₁² ⋊ C₂²×C₉
Hall	C₇⋊(C₁₁²⋊C₉) ⋊ C₂²
Hall	C₂×C₁₁²×D₇ ⋊ C₉
Sylow	C₁₁² ⋊ C₂×D₇⋊C₉
Hall	C₂×D₇ ⋊ C₁₁²⋊C₉
Sylow	C₇ ⋊ C₂²×C₁₁²⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇⋊(C₁₁²⋊C₃)
commutator, hypocenter	C₇×C₁₁²	C₂²×C₉
Frattini	C₃	C₂×D₇⋊(C₁₁²⋊C₃)
Fitting, socle	C₂×C₃×C₇×C₁₁²	C₂×C₃
prime radical	C₂×C₃×C₁₁²×D₇	C₃
cosocle	C₃×C₇×C₁₁²	C₂²×C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₂×C₃

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1386

Conjugacy classes & character table

1242 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 166);