D₁₀₉₂₅ #36345795

order	21850
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₀₉₂₅
unambiguous semidirect product	C₁₉⋊D₅₇₅
unambiguous semidirect product	C₂₃⋊D₄₇₅
unambiguous semidirect product	C₂₅⋊D₄₃₇

Splittings

Fitting, derived, Hall	C₁₉×C₂₃×C₂₅ ⋊ C₂
Hall	C₂₃×C₂₅ ⋊ D₁₉
Hall	C₁₉×C₂₅ ⋊ D₂₃
Hall	C₁₉×C₂₃ ⋊ D₂₅
Sylow	C₂₅ ⋊ D₄₃₇
Sylow	C₂₃ ⋊ D₄₇₅
Sylow	C₁₉ ⋊ D₅₇₅

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₉×C₂₃×C₂₅	C₂
Frattini	C₅	D₂₁₈₅
socle	C₅×C₁₉×C₂₃	D₅
LCS	G ▷ C₁₉×C₂₃×C₂₅
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 10925

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

Polycyclic presentation:

2,5,19,23,5|b^5=e^4,b^a=b^4e,c^a=c^18,d^a=d^22,e^a=e^4

Conjugacy classes & character table

5464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21850, 8);

D10925 #36345795