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C₂×C₇×(C₇⋊C₉)⋊D₁₃ #37524510

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×(C₇⋊C₉)⋊D₁₃
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊(C₇×D₁₃)

Splittings

derived	C₇×C₁₃ ⋊ C₂²×C₇×C₉
Hall	C₇×C₁₃×C₇⋊C₉ ⋊ C₂²
Hall	C₂×C₇×D₉₁ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₂²×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₂×D₁₃
Sylow	C₇² ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×C₇×D₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	ΓL(1,𝔽₈)⋊D₁₃
commutator, hypocenter	C₇×C₁₃	C₂²×C₇×C₉
Frattini	C₃	C₂×C₇×ΓL(1,𝔽₈)⋊D₁₃
Fitting, socle	C₂×C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₇×D₉₁	C₃
cosocle	C₃×C₇×C₁₃	C₂²×C₃×C₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₃×C₇

128 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3276

Conjugacy classes & character table

1554 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 455);