C₁₃×Dic₃₈₇ #34117407

order	20124
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₃₈₇
unambiguous semidirect product	C₉⋊(C₁₃×Dic₄₃)
unambiguous semidirect product	C₄₃⋊(C₁₃×Dic₉)

Splittings

derived, Hall	C₉×C₄₃ ⋊ C₄×C₁₃
Hall	C₉×C₁₃×C₄₃ ⋊ C₄
Hall	C₁₃×C₄₃ ⋊ Dic₉
Hall	C₉×C₁₃ ⋊ Dic₄₃
Sylow	C₄₃ ⋊ C₁₃×Dic₉
Sylow	C₉ ⋊ C₁₃×Dic₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₃₈₇
commutator, hypocenter	C₉×C₄₃	C₄×C₁₃
Frattini	C₂×C₃	C₁₃×D₁₂₉
Fitting	C₂×C₉×C₁₃×C₄₃	C₂
socle, prime radical	C₂×C₃×C₁₃×C₄₃	D₃
cosocle	C₂×C₉×C₄₃	C₂×C₁₃
LCS	G ▷ C₉×C₄₃
UCS	C₁ ◁ C₂×C₁₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 20124

A minimal faithful permutation representation — 2 generators on 69 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)(53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69);(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)(44,49,47,46,51,48,50,45,52)

Conjugacy classes & character table

5070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 10);

C13×Dic387 #34117407