Finite Group Databasebeta

#23748717

order9488
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC593 ⋊ M16

Subgroups

subgroupG/H
center, FrattiniC4C2×D593
commutator, socleC2×C593C2×C4
FittingC2×C4×C593C2
prime radicalC22×C593C4
cosocleC4×C593C22
hypercenterC2×C4D593
hypocenterC593M16
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C4 ◁ C2×C4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

2378 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34039201, #34039202, #34039203, …
maximal normal subgroup of#34039201, #34039202, #34039203, …
maximal quotient of#34039196, C22⋊#18011654, C4⋊#18011654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9488, 24);