Finite Group Databasebeta

#37560622

order23888
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1493 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D1493
commutator, cosocleC4×C1493C22
FrattiniC4C2×D1493
Fitting, prime radicalD4×C1493C2
socleC2×C1493D4
hypercenterD4D1493
hypocenterC1493SD16
LCSG ▷ C4×C1493 ▷ C2×C1493 ▷ C1493
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11944

Polycyclic presentation:

2^4,1493|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1492,c^b=cd

Conjugacy classes & character table

3737 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23888, 28);