Finite Group Databasebeta

#23748721

order9488
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC593 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D593
commutator, cosocleC4×C593C22
FrattiniC4C2×D593
Fitting, prime radicalD4×C593C2
socleC2×C593D4
hypercenterD4D593
hypocenterC593SD16
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^4,593|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^592,c^b=cd

Conjugacy classes & character table

1487 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofSD16×D593, C2×#23748721, #34039304, …
maximal normal subgroup ofSD16×D593, C2×#23748721, #34039304, …
maximal quotient of#34039206, #34039208, #34039216, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9488, 28);