D₁₄₈₀₇ #44444149

order	29614
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₈₀₇
unambiguous semidirect product	C₁₃⋊D₁₁₃₉
unambiguous semidirect product	C₁₇⋊D₈₇₁
unambiguous semidirect product	C₆₇⋊D₂₂₁

Splittings

Fitting, socle, derived, Hall	C₁₃×C₁₇×C₆₇ ⋊ C₂
Hall	C₁₇×C₆₇ ⋊ D₁₃
Hall	C₁₃×C₆₇ ⋊ D₁₇
Hall	C₁₃×C₁₇ ⋊ D₆₇
Sylow	C₆₇ ⋊ D₂₂₁
Sylow	C₁₇ ⋊ D₈₇₁
Sylow	C₁₃ ⋊ D₁₁₃₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₆₇	C₂
LCS	G ▷ C₁₃×C₁₇×C₆₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 14807

A minimal faithful permutation representation — 2 generators on 97 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)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Polycyclic presentation:

2,13,17,67|b^a=b^12,c^a=c^16,d^a=d^66

Conjugacy classes & character table

7405 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₈₀₇
maximal normal subgroup of	C₂×D₁₄₈₀₇
maximal quotient of	Dic₁₄₈₀₇, C₂×D₁₄₈₀₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29614, 8);

D14807 #44444149