C₃²×D₁₅₅ #14584080

order	2790
isoclinism	isoclinic class of D₁₅₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×D₁₅₅
unambiguous semidirect product	C₅⋊(C₃²×D₃₁)

Splittings

Fitting, socle, Hall	C₃²×C₅×C₃₁ ⋊ C₂
derived, Hall	C₅×C₃₁ ⋊ C₂×C₃²
Hall	C₃²×C₃₁ ⋊ D₅
Hall	C₃²×C₅ ⋊ D₃₁
Sylow	C₃₁ ⋊ C₃²×D₅
Sylow	C₅ ⋊ C₃²×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	D₁₅₅
commutator, cosocle, hypocenter	C₅×C₃₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₁	C₂
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₃²

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1395

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3)(7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42);(4,5,6)(8,11)(9,10)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃²×D₇₇₅, C₃²×C₅⋊(D₃₁⋊C₅), C₃²×C₅⋊D₁₅₅, …
maximal normal subgroup of	C₃²×C₅⋊(D₃₁⋊C₅), C₃²×C₅×D₁₅₅, C₃²×C₇×D₁₅₅, …
maximal quotient of	C₃²×D₇₇₅, C₃²×C₅⋊D₁₅₅, C₃²×C₅×D₁₅₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2790, 40);

C32×D155 #14584080