Finite Group Databasebeta

#23748710

order9488
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

FittingC2×C4×C593 ⋊ C2
SylowC593 ⋊ C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C2×D593
commutatorC2×C593C2×C4
FittingC2×C4×C593C2
socle, cosocleC22×C593C22
prime radicalC22×D593C2
hypercenterC2×C4D593
hypocenterC593C22⋊C4
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C22 ◁ C2×C4

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22⋊C4×D593, C2×#23748710, #34039242, …
maximal normal subgroup ofC22⋊C4×D593, C2×#23748710, #34039242, …
maximal quotient of#34039192, #34039197, #34039199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9488, 17);