Finite Group Databasebeta

#44470668

order29888
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #544

Subgroups

subgroupG/H
center, FrattiniC22C23×D467
commutator, socle, cosocleC22×C467C24
FittingC2×C4⋊C4×C467C2
prime radicalC23×C467C23
hypercenterC2×C4⋊C4D467
hypocenterC467#544
LCSG ▷ C22×C467 ▷ C467
UCSC1 ◁ C22 ◁ C2×C4⋊C4

206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Polycyclic presentation:

2^6,467|a^2=f,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^466,c^b=ce

Conjugacy classes & character table

4682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1180);