C₃×Dic₃₄ #87978

order	408
isoclinism	isoclinic class of Dic₃₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₃₄
unambiguous semidirect product	C₁₇⋊(C₃×Q₈)

Splittings

Hall	C₃×C₁₇ ⋊ Q₈
Sylow	C₁₇ ⋊ C₃×Q₈

Subgroups

	subgroup	G/H
center	C₂×C₃	C₂×D₁₇
commutator, cosocle	C₂×C₁₇	C₂²×C₃
Frattini	C₂	C₂×C₃×D₁₇
Fitting	C₃×C₄×C₁₇	C₂
socle, prime radical	C₂×C₃×C₁₇	C₂²
hypercenter	C₃×C₄	D₁₇
hypocenter	C₁₇	C₃×Q₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3)(4,5,6,7)(8,11,10,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28);(4,8,6,10)(5,9,7,11)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11717747, #11717749, #11717752, …
maximal normal subgroup of	#11717747, #11717749, #11717752, …
maximal quotient of	C₃×#63225, C₃×C₄⋊Dic₁₇, C₂×C₃×Dic₃₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 15);

C3×Dic34 #87978

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₃×Dic₃₄ #87978