Finite Group Databasebeta

← Prev (#37524513) Next (#37524515) →

C₂×C₇×(C₁₃⋊C₉)⋊D₇ #37524514

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

Aliases

direct product	C₂×C₇×(C₁₃⋊C₉)⋊D₇
unambiguous semidirect product	(C₂×C₁₃⋊C₉)⋊(C₇×D₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	(C₁₃⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₁₃	C₂²×C₇×C₉
Frattini	C₃	C₂×C₇×(C₁₃⋊C₃)⋊D₇
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

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

normal subgroups only

This group has 156 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

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 459);