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C₂×(C₉₇⋊C₉)⋊D₇ #37567785

order	24444
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₉₇⋊C₉)⋊D₇
unambiguous semidirect product	(C₂×C₉₇⋊C₉)⋊D₇

Splittings

derived, Hall	C₇×C₉₇ ⋊ C₂²×C₉
Hall	C₇×C₉₇⋊C₉ ⋊ C₂²
Hall	C₂×D₆₇₉ ⋊ C₉
Hall	C₉₇⋊C₉ ⋊ C₂×D₇
Sylow	C₉₇ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×D₉₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₉₇⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₉₇	C₂²×C₉
Frattini	C₃	C₂×(C₉₇⋊C₃)⋊D₇
Fitting, socle	C₂×C₃×C₇×C₉₇	C₂×C₃
prime radical	C₂×C₃×D₆₇₉	C₃
cosocle	C₃×C₇×C₉₇	C₂²×C₃
LCS	G ▷ C₇×C₉₇
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12222

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 48);