C₂₇×Dic₁₄ #13094127

order	1512
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₇ · Schur multiplier (H₂) = C₁

metacyclic
supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₂₇×Dic₁₄

Splittings

Hall	C₇×C₂₇ ⋊ Q₈
Sylow	C₇ ⋊ Q₈×C₂₇

Subgroups

	subgroup	G/H
center	C₂×C₂₇	C₂×D₇
commutator	C₂×C₇	C₂²×C₂₇
Frattini	C₂×C₉	C₂×C₃×D₇
Fitting	C₄×C₇×C₂₇	C₂
socle, prime radical	C₂×C₃×C₇	C₂²×C₉
cosocle	C₂×C₇×C₉	C₂²×C₃
hypercenter	C₄×C₂₇	D₇
hypocenter	C₇	Q₈×C₂₇
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₂₇ ◁ C₄×C₂₇

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1512

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 24);

C27×Dic14 #13094127