Finite Group Databasebeta

#44470227

order29888
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #458

Subgroups

subgroupG/H
centerC2#28417922
commutator, cosocleC23×C467C23
FrattiniC23C22×D467
Fitting, prime radicalH(5,𝔽2)×C467C2
socleC2×C467#120
hypercenterH(5,𝔽2)D467
hypocenterC467#458
LCSG ▷ C23×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2 ◁ C23 ◁ H(5,𝔽2)

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7472

Polycyclic presentation:

2^6,467|a^2=f,b^a=bd,c^a=ce,g^a=g^466,e^b=ef,d^c=df

Conjugacy classes & character table

3977 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 739);