D₁₅₄₅₇ #44525646

order	30914
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₄₅₇
unambiguous semidirect product	C₁₃⋊D₁₁₈₉
unambiguous semidirect product	C₂₉⋊D₅₃₃
unambiguous semidirect product	C₄₁⋊D₃₇₇

Splittings

Fitting, socle, derived, Hall	C₁₃×C₂₉×C₄₁ ⋊ C₂
Hall	C₂₉×C₄₁ ⋊ D₁₃
Hall	C₁₃×C₄₁ ⋊ D₂₉
Hall	C₁₃×C₂₉ ⋊ D₄₁
Sylow	C₄₁ ⋊ D₃₇₇
Sylow	C₂₉ ⋊ D₅₃₃
Sylow	C₁₃ ⋊ D₁₁₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₂₉×C₄₁	C₂
LCS	G ▷ C₁₃×C₂₉×C₄₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 15457

A minimal faithful permutation representation — 2 generators on 83 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)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(44,83)(45,82)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)

Polycyclic presentation:

2,13,29,41|b^a=b^12,c^a=c^28,d^a=d^40

Conjugacy classes & character table

7730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₄₅₇
maximal normal subgroup of	C₂×D₁₅₄₅₇
maximal quotient of	Dic₁₅₄₅₇, C₂×D₁₅₄₅₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30914, 8);

D15457 #44525646