Finite Group Databasebeta

← Prev (#21440347) Next (#21440349) →

Dic1925 #21440348

order7700
automorphismAut(G) order 4620000
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic1925
unambiguous semidirect productC7⋊Dic275
unambiguous semidirect productC11⋊Dic175

Splittings

derived, HallC7×C11×C25 ⋊ C4
HallC11×C25 ⋊ Dic7
HallC7×C25 ⋊ Dic11
HallC7×C11 ⋊ Dic25
SylowC25 ⋊ Dic77
SylowC11 ⋊ Dic175
SylowC7 ⋊ Dic275

Subgroups

subgroupG/H
center, hypercenterC2D1925
commutator, hypocenterC7×C11×C25C4
FrattiniC2×C5D385
FittingC2×C7×C11×C25C2
socleC2×C5×C7×C11D5
LCSG ▷ C7×C11×C25
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×Dic1925, Dic5775, C11⋊(ΓL(1,𝔽8)⋊Dic25), …
maximal normal subgroup ofC3×Dic1925, C11⋊(ΓL(1,𝔽8)⋊Dic25), Dic3850
maximal quotient ofC3×Dic1925, Dic5775, Dic9625, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 12);