Finite Group Databasebeta

#44470342

order29888
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #479

Subgroups

subgroupG/H
centerC22D4×D467
commutator, cosocleC2×C4×C467C23
FrattiniC2×C4C22×D467
Fitting#103×C467C2
socle, prime radicalC22×C467C2×D4
hypercenter#103D467
hypocenterC467#479
LCSG ▷ C2×C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Polycyclic presentation:

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

Conjugacy classes & character table

3281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 854);