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C₂×(C₇₉⋊C₉)⋊D₇ #34092579

order	19908
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₇₉⋊C₉)⋊D₇
unambiguous semidirect product	(C₂×C₇₉⋊C₉)⋊D₇

Splittings

derived, Hall	C₇×C₇₉ ⋊ C₂²×C₉
Hall	C₇×C₇₉⋊C₉ ⋊ C₂²
Hall	C₂×D₅₅₃ ⋊ C₉
Hall	C₇₉⋊C₉ ⋊ C₂×D₇
Sylow	C₇₉ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×D₇₉⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₇₉⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₇₉	C₂²×C₉
Frattini	C₃	C₂×(C₇₉⋊C₃)⋊D₇
Fitting, socle	C₂×C₃×C₇×C₇₉	C₂×C₃
prime radical	C₂×C₃×D₅₅₃	C₃
cosocle	C₃×C₇×C₇₉	C₂²×C₃
LCS	G ▷ C₇×C₇₉
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9954

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19908, 40);