D₁₃×D₃₈₇ #34117455

order	20124
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₁₃×D₃₈₇
unambiguous semidirect product	(C₉×D₁₃)⋊D₄₃
unambiguous semidirect product	(D₁₃×C₄₃)⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₃×C₄₃ ⋊ C₂²
Hall	C₁₃×C₄₃ ⋊ C₂×D₉
Hall	C₉×C₄₃ ⋊ C₂×D₁₃
Hall	C₉×C₁₃ ⋊ C₂×D₄₃
Sylow	C₄₃ ⋊ D₉×D₁₃
Sylow	C₁₃ ⋊ C₂×D₃₈₇
Sylow	C₉ ⋊ D₁₃×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃×C₄₃	C₂²
Frattini	C₃	D₁₃×D₁₂₉
socle	C₃×C₁₃×C₄₃	C₂×D₃
LCS	G ▷ C₉×C₁₃×C₄₃
UCS	C₁

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 5031

A minimal faithful permutation representation — 2 generators on 65 points:

(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)(45,47)(46,50)(48,51)(49,52)(53,54,56,58,60,62,64,65,63,61,59,57,55);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(44,51,52,46,45,47,50,49,48)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 58);

D13×D387 #34117455