Finite Group Databasebeta

D3184 #20263897

order6368
automorphismAut(G) order 5043456
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD3184

Splittings

FittingC16×C199 ⋊ C2
SylowC199 ⋊ D16

Subgroups

subgroupG/H
centerC2D1592
commutatorC8×C199C22
FrattiniC8C2×D199
FittingC16×C199C2
socleC2×C199D8
hypercenterC16D199
hypocenterC199D16
LCSG ▷ C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^5,199|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^198,c^b=cd,d^b=de,f^b=f^198

Conjugacy classes & character table

1595 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#27163853, D6368, #27163855, …
maximal normal subgroup of#27163853, D6368, #27163855, …
maximal quotient of#27163820, #27163844, D6368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6368, 88);