D₁₄₇₂₅ #44441291

order	29450
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₇₂₅
unambiguous semidirect product	C₁₉⋊D₇₇₅
unambiguous semidirect product	C₂₅⋊D₅₈₉
unambiguous semidirect product	C₃₁⋊D₄₇₅

Splittings

Fitting, derived, Hall	C₁₉×C₂₅×C₃₁ ⋊ C₂
Hall	C₂₅×C₃₁ ⋊ D₁₉
Hall	C₁₉×C₃₁ ⋊ D₂₅
Hall	C₁₉×C₂₅ ⋊ D₃₁
Sylow	C₃₁ ⋊ D₄₇₅
Sylow	C₂₅ ⋊ D₅₈₉
Sylow	C₁₉ ⋊ D₇₇₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₉×C₂₅×C₃₁	C₂
Frattini	C₅	D₂₉₄₅
socle	C₅×C₁₉×C₃₁	D₅
LCS	G ▷ C₁₉×C₂₅×C₃₁
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 14725

A minimal faithful permutation representation — 2 generators on 75 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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Polycyclic presentation:

2,5,19,31,5|b^5=e^4,b^a=b^4e,c^a=c^18,d^a=d^30,e^a=e^4

Conjugacy classes & character table

7364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₇₂₅
maximal normal subgroup of	C₂×D₁₄₇₂₅
maximal quotient of	Dic₁₄₇₂₅, C₂×D₁₄₇₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29450, 9);

D14725 #44441291