C₁₃×Dic₂₈ #13089798

order	1456
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×Dic₂₈

Splittings

Hall	C₇×C₁₃ ⋊ Q₁₆
Sylow	C₇ ⋊ C₁₃×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₃	D₂₈
commutator, cosocle	C₄×C₇	C₂²×C₁₃
Frattini	C₄	C₂×C₁₃×D₇
Fitting	C₇×C₈×C₁₃	C₂
socle, prime radical	C₂×C₇×C₁₃	D₄
hypercenter	C₈×C₁₃	D₇
hypocenter	C₇	C₁₃×Q₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₈×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1456

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 52);

C13×Dic28 #13089798