D₃×(C₂²⋊C₂₇)⋊C₂ #13048063

order	1296
isoclinism	isoclinic class of D₃×(C₂²⋊C₂₇)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₃×(C₂²⋊C₂₇)⋊C₂
unambiguous semidirect product	(C₃×(C₂²⋊C₂₇)⋊C₂)⋊C₂
unambiguous semidirect product	(C₃⋊((C₂²⋊C₂₇)⋊C₂))⋊C₂
unambiguous semidirect product	(D₃×C₂²⋊C₂₇)⋊C₂

C₃×C₂²⋊C₂₇ ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₂²⋊C₂₇	C₂²
Frattini	C₉	D₃×S₄
Fitting	C₂²×C₃×C₉	C₂×D₃
socle	C₂²×C₃²	C₂×D₉
LCS	G ▷ C₃×C₂²⋊C₂₇
UCS	C₁

176 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

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

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1781);