D₁₁₉₇₇ #37561718

order	23954
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₉₇₇
unambiguous semidirect product	C₇⋊D₁₇₁₁
unambiguous semidirect product	C₂₉⋊D₄₁₃
unambiguous semidirect product	C₅₉⋊D₂₀₃

Splittings

Fitting, socle, derived, Hall	C₇×C₂₉×C₅₉ ⋊ C₂
Hall	C₂₉×C₅₉ ⋊ D₇
Hall	C₇×C₅₉ ⋊ D₂₉
Hall	C₇×C₂₉ ⋊ D₅₉
Sylow	C₅₉ ⋊ D₂₀₃
Sylow	C₂₉ ⋊ D₄₁₃
Sylow	C₇ ⋊ D₁₇₁₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₉×C₅₉	C₂
LCS	G ▷ C₇×C₂₉×C₅₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 11977

A minimal faithful permutation representation — 2 generators on 95 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);(2,7)(3,6)(4,5)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,95)(39,94)(40,93)(41,92)(42,91)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)

Polycyclic presentation:

2,7,29,59|b^a=b^6,c^a=c^28,d^a=d^58

Conjugacy classes & character table

5990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23954, 10);

D11977 #37561718