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D1925 #16838673

order3850
automorphismAut(G) order 2310000
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD1925
unambiguous semidirect productC7⋊D275
unambiguous semidirect productC11⋊D175
unambiguous semidirect productC25⋊D77

Splittings

Fitting, derived, HallC7×C11×C25 ⋊ C2
HallC11×C25 ⋊ D7
HallC7×C25 ⋊ D11
HallC7×C11 ⋊ D25
SylowC25 ⋊ D77
SylowC11 ⋊ D175
SylowC7 ⋊ D275

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C11×C25C2
FrattiniC5D385
socleC5×C7×C11D5
LCSG ▷ C7×C11×C25
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1925

A minimal faithful permutation representation — 2 generators on 43 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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(27,32)(28,31)(29,30)(34,43)(35,42)(36,41)(37,40)(38,39)

Polycyclic presentation:

2,5,7,11,5|b^5=e^4,b^a=b^4e,c^a=c^6,d^a=d^10,e^a=e^4

Conjugacy classes & character table

964 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D1925, D5775, C11⋊(ΓL(1,𝔽8)⋊D25), …
maximal normal subgroup ofC3×D1925, C11⋊(ΓL(1,𝔽8)⋊D25), C7×D1925
maximal quotient ofC3×D1925, D5775, D13475, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3850, 12);