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C₂×(C₆₇⋊C₉)⋊D₁₃ #44535612

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

Aliases

direct product	C₂×(C₆₇⋊C₉)⋊D₁₃
unambiguous semidirect product	(C₂×C₆₇⋊C₉)⋊D₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₆₇⋊C₃)⋊D₁₃
commutator, hypocenter	C₁₃×C₆₇	C₂²×C₉
Frattini	C₃	C₂×(C₆₇⋊C₃)⋊D₁₃
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

1002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 48);