C₁₃×Dic₂₇ #13063871

order	1404
isoclinism	isoclinic class of D₂₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₂₇
unambiguous semidirect product	C₂₇⋊(C₄×C₁₃)

Splittings

derived, Sylow	C₂₇ ⋊ C₄×C₁₃
Hall	C₁₃×C₂₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₂₇
commutator, hypocenter	C₂₇	C₄×C₁₃
Frattini	C₂×C₉	D₃×C₁₃
Fitting	C₂×C₁₃×C₂₇	C₂
socle, prime radical	C₂×C₃×C₁₃	D₉
cosocle	C₂×C₂₇	C₂×C₁₃
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₂×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1404

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(14,16,15,17)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 3);

C13×Dic27 #13063871