Finite Group Databasebeta

#19143059

order5504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #2884

Subgroups

subgroupG/H
centerC2C22×C22⋊Dic43
commutatorC22×C43C23×C4
FrattiniC23C23×D43
FittingC2×2−1+4×C43C2
socleC2×C43C22×C22⋊C4
hypercenterC2×2−1+4D43
hypocenterC43#2884
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×Q8 ◁ C2×2−1+4

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^7,43|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^42,f^b=fg,d^c=dg

Conjugacy classes & character table

755 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#25014189, #25014193, #25014203, …
maximal normal subgroup of#25014189, #25014193, #25014203, …
maximal quotient of#25062426, #25062430, #25062530, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5504, 12974);