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C₂×(C₁₃⋊C₉)⋊D₆₇ #44535608

order	31356
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₁₃⋊C₉)⋊D₆₇
unambiguous semidirect product	(C₂×C₁₃⋊C₉)⋊D₆₇

Splittings

derived, Hall	C₁₃×C₆₇ ⋊ C₂²×C₉
Hall	C₆₇×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×D₈₇₁ ⋊ C₉
Hall	C₁₃⋊C₉ ⋊ C₂×D₆₇
Sylow	C₆₇ ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×C₉×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₃⋊C₃)⋊D₆₇
commutator, hypocenter	C₁₃×C₆₇	C₂²×C₉
Frattini	C₃	C₂×(C₁₃⋊C₃)⋊D₆₇
Fitting, socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₈₇₁	C₃
cosocle	C₃×C₁₃×C₆₇	C₂²×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15678

Conjugacy classes & character table

1434 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 44);