C₁₃×Dic₂₄ #11928072

order	1248
isoclinism	isoclinic class of D₄₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×Dic₂₄

Splittings

Hall	C₃×C₁₃ ⋊ Q₃₂
Sylow	C₃ ⋊ C₁₃×Q₃₂

Subgroups

	subgroup	G/H
center	C₂×C₁₃	D₂₄
commutator, cosocle	C₃×C₈	C₂²×C₁₃
Frattini	C₈	C₂×D₃×C₁₃
Fitting	C₃×C₁₃×C₁₆	C₂
socle, prime radical	C₂×C₃×C₁₃	D₈
hypercenter	C₁₃×C₁₆	D₃
hypocenter	C₃	C₁₃×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ C₈×C₁₃ ◁ C₁₃×C₁₆

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 1248

A minimal faithful permutation representation — 2 generators on 48 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)(30,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31)(46,47,48);(14,30,22,38)(15,31,23,39)(16,32,24,40)(17,33,25,41)(18,34,26,42)(19,35,27,43)(20,36,28,44)(21,37,29,45)(47,48)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 184);

C13×Dic24 #11928072